Overview
This chapter introduces Class 6 students to basic data handling: how to collect, record, organize and represent information so it becomes meaningful. Importance: Data handling helps students read everyday information (like school attendance, survey results), make comparisons, spot patterns and draw simple conclusions — a foundational skill for numeracy and problem solving. Key themes: methods of collecting data; organizing data using tally marks and frequency tables; representing data with pictographs and bar graphs; choosing and using an appropriate scale; reading and interpreting graphs to answer questions. What the student will learn: recognise different types of data, record observations systematically, convert raw data into organized tables, draw and use pictographs (including understanding and applying a given picture-scale), construct and interpret bar graphs, compare data sets and answer questions based on graphical information, and develop basic reasoning skills for making inferences from data.
Learning Objectives
- Define data and related terms such as observation, frequency, and category.
- Distinguish between qualitative and quantitative data with examples.
- Collect and record data from surveys and experiments using tally marks.
- Organize recorded data into frequency tables to facilitate analysis.
- Construct pictographs using a suitable scale to represent given data.
- Draw bar graphs with labelled axes and appropriate scales to display data.
- Convert between tally marks, frequency tables, pictographs, and bar graphs.
- Calculate the mode from a frequency distribution and interpret its meaning.
Topics in this chapter
8 topics · tap a topic title to jump straight to it.
Introduction to Data Handling
What is Data? Data are facts, numbers or information collected for a particular purpose — for example, test scores, number of students who like a fruit, or temperatures recorded over a week.
Why learn Data Handling? To collect, organise, represent and interpret information so we can answer questions, make decisions and spot patterns.
Steps in Data Handling
- Collect the data (ask questions, conduct a survey or record measurements).
- Organise the data into a tally chart or frequency table so the information is clear and compact.
- Represent the organised data using simple graphs like pictographs or bar graphs.
- Interpret the graph to draw conclusions (which is most/least, how many more, etc.).
Common terms
- Observation — one item of data (e.g., one student's choice).
- Category/class — group into which observations fall (e.g., apples, bananas).
- Frequency — number of observations in a category.
- Tally — quick marks used to count observations in groups of five.
Organising data — Tally and Frequency Table
Use tally marks (|||| = 4, ||||/ = 5) to record counts while collecting. Convert tallies to a frequency table listing each category and its frequency. This table is the basis for drawing graphs.
Representing data — Pictograph and Bar Graph
Pictograph: use pictures or symbols to represent a fixed number of items. Always provide a key (for example: one apple symbol = 2 students). Bar Graph: use bars (vertical or horizontal) whose heights/lengths represent frequency. Label axes, choose a suitable scale, give a title and include a key if needed.
Reading and interpreting — Compare bars or symbols to answer questions (Which is most popular? How many more?). You can also compute simple measures such as the total, range or average for numerical data.
- Example 1 — Favourite fruits (survey of 30 students): Data collected: Apples, Bananas, Mangoes, Grapes. Make a tally and frequency table, then draw a pictograph. Suppose tally results: Apples ||||/ || (7), Bananas ||||/ |||| (9), Mangoes ||||/ ||||/ (11), Grapes |||| (4). Frequency table: Apples 7, Bananas 9, Mangoes 11, Grapes 3 (adjust to total 30). Pictograph key: 1 fruit symbol = 1 student. From the pictograph we can answer: most students like Mangoes, how many more like Mangoes than Grapes (11 − 3 = 8), etc.
- Example 2 — Books read in a month by 8 students: Data: 2, 5, 3, 4, 5, 2, 6, 3. Frequency table: 2→2, 3→2, 4→1, 5→2, 6→1. Draw a vertical bar graph with 'Number of books' on the x-axis and 'Number of students' on the y-axis. Calculate range = 6 − 2 = 4. Mean = (2+5+3+4+5+2+6+3) / 8 = 30 / 8 = 3.75 books (average).
- Example 3 — Temperatures for a week (°C): 30, 32, 31, 29, 30, 33, 31. Organise into a table and draw a bar graph. Frequency: 29→1, 30→2, 31→2, 32→1, 33→1. Range = 33 − 29 = 4°C. Use the graph to spot warmest and coolest days and how many days had temperature 31°C (2 days).
- Frequency of a category = Number of occurrences of that category
- Total frequency = Sum of frequencies of all categories
- Mean (average) = (Sum of all observations) / (Number of observations)
- Range = Maximum value − Minimum value
- Percentage for a category = (Frequency / Total) × 100
Recording Data
What is Recording Data?
Recording data means writing down observations or measurements in an organised way so they can be counted, compared and represented. Good recording turns raw information into a form that is easy to read and use for drawing conclusions.
Steps to record data
- Decide what to observe and for how long (e.g., number of students with pets in a class).
- Collect the observations carefully (ask each student or measure each item).
- Organise the observations using tally marks or a table (this prevents mistakes).
- Convert the tally table into a frequency table showing how often each value occurs.
- Represent the frequency table with a pictograph or bar graph for clear visual comparison.
Common recording tools
- Tally marks: quick grouping method (group in 5s like ||||\ for easy counting).
- Frequency table: lists categories/values and their frequencies.
- Pictograph: uses pictures or symbols with a key (for example, one apple symbol = 2 students).
- Bar graph: bars show frequencies; bars are of equal width and spaced equally.
Why it matters
Recording data carefully avoids errors, makes patterns easy to see (most common, least common), and provides the basis for further work like finding averages or drawing conclusions.
Short example (in words)
Suppose you ask 24 students which fruit they like best. You record each answer using tally marks as you ask. Then you convert tallies to numbers (frequency), and draw a bar graph to show which fruit is most popular.
- Count of pets in a class: Ask each student how many pets they have, mark tallies, make a frequency table, then draw a bar graph showing how many students have 0, 1, 2, 3... pets.
- Favourite fruits of 30 students: Record each answer with tally marks (grouping in 5s), convert to frequencies, make a pictograph with a key (for example 1 fruit icon = 2 students).
- Books read in a month by students: Note numbers for each student, sort into a frequency table (0,1,2,3...), and draw a bar graph to compare reading habits.
- Number of rainy days in each month: Record the count for each month and present the data in a simple table and a bar graph to compare months.
- Shoe sizes in a class: Tally each reported size, create a frequency table and use a bar graph to show the most common sizes.
- Total frequency (N) = sum of all individual frequencies = f1 + f2 + f3 + ...
- Relative frequency of a category = fi / N (gives a fraction of the total)
- Percentage for a category = (fi / N) × 100%
- Check: sum of all relative frequencies = 1 (or 100%)
Tally Marks and Frequency
What are tally marks? Tally marks are a simple way to keep a running count of items by marking one vertical line for each observation and grouping every fifth observation with a diagonal or a slash. This makes counting large numbers quick and error-free. Example of grouping: 1= |, 2= ||, 3= |||, 4= ||||, 5= ||||/ (the slash or diagonal crosses the previous four).
What is frequency? Frequency is the number of times a particular item or category occurs in a set of data. Tally marks are used as an intermediate step to produce a frequency table.
How to make a tally-and-frequency table (step-by-step):
- List the categories (e.g., colours, fruits, sports).
- For each observation, add one vertical tally mark in the appropriate category.
- Group every fifth observation by drawing a slash (or diagonal) across the previous four to form a group of five.
- Count the tally marks (groups of five make counting quick) and record the frequency for each category.
- Use the frequency values to draw graphs (bar graph, pictograph, pie chart).
Small example (favorite fruits of 20 students):
| Fruit | Tally | Frequency |
|---|---|---|
| Apple | ||||/|| | 7 |
| Banana | ||||/| | 6 |
| Mango | |||| | 4 |
| Orange | ||| | 3 |
| Total | 20 |
Tips and common points: use tally marks while collecting data (surveys, classroom counts) because they reduce counting mistakes; always group in fives for fast counting; transfer tally totals to a frequency column before drawing graphs.
- Classroom survey: 30 students were asked their favourite sport. Use tally marks while asking and then write the frequency of each sport (Cricket: ||||/|| = 7, Football: ||||/||| = 8, Badminton: |||| = 4, Others: ||| = 3).
- Traffic study: Count colours of cars passing a gate for 1 hour. Record each car with a tally mark under its colour category, then find frequencies to know the most common car colour.
- Library use: Keep a tally of how many students borrow different types of books (Story, Science, Maths, Comics) over a week; convert tallies to frequencies to plan purchases.
- Class votes: For class monitor election, mark each vote with a tally beside the candidate’s name; convert tallies to frequencies to see who won.
- Frequency of a category = Number of observations in that category (obtained by counting tally marks).
- Total number of observations = Sum of frequencies of all categories.
- Relative frequency = Frequency of a category / Total number of observations.
- Percentage frequency = (Frequency / Total) × 100.
- Cumulative frequency (for ordered data) = Running total of frequencies up to a given category.
Organising Data (Frequency Table)
What is a frequency table? A frequency table organises raw data by listing each value (or class of values) together with the number of times it occurs. The number of occurrences is called the frequency.
Why use it? It makes large or messy data easy to read, compare and use for drawing graphs.
Steps to make a simple frequency table (for discrete data):
- Collect the raw data (e.g., marks, counts, choices).
- List each distinct value in one column (called the data value or class).
- Use tally marks to count how many times each value occurs.
- Write the total tally count for each value in the frequency column.
- Check that the sum of frequencies equals the total number of observations.
Grouped data and class intervals: When data has many different values (or continuous measurements), group values into class intervals (e.g., 10–19, 20–29). For each interval count how many data points fall into it and record the frequency. Choose intervals that are equal in width and cover all data without overlap.
Tally marks help avoid counting errors. Use four vertical marks and a diagonal fifth mark across them (|||| = 4, ||||\ = 5) and then sum the groups.
Checks and extra columns: You may add columns like cumulative frequency (running total), relative frequency (proportion), or percentage frequency to better understand the data.
- Example 1 (marks): Students' scores out of 10: 7, 5, 8, 7, 10, 5, 7. Frequency table: Value: 5, Frequency: 2; 7 → 3; 8 → 1; 10 → 1.
- Example 2 (favourite fruit - categorical): 12 students chose apple, 8 chose banana, 5 chose mango. Table: Fruit | Frequency → Apple:12, Banana:8, Mango:5.
- Example 3 (grouped data - ages): Ages of children: many values from 6 to 12. Class intervals: 6–7, 8–9, 10–11, 12–13. Count how many fall in each interval and record frequency.
- Example 4 (real-life - shoe sizes): Collect shoe sizes of a class and make a frequency table to see which size is most common.
- Frequency of a value/class: f (count of observations in that value or class).
- Total number of observations: N = Σf (sum of all frequencies).
- Relative frequency: r = f / N (proportion of total).
- Percentage frequency: % = (f / N) × 100.
- Cumulative frequency (up to class k): CF_k = Σ (frequencies of classes up to k).
Pictographs (Pictograms)
What is a pictograph?
A pictograph (or pictogram) is a method of representing numerical data using pictures or symbols. Each picture (or symbol) stands for a fixed number of items (this fixed number is called the scale or value of one symbol).
Key ideas
- Scale/Key: Always state the key, for example: 1 symbol = 5 students. The key tells how many units each symbol represents.
- Counting symbols: To find the actual number from a pictograph, count symbols and multiply by the scale. If part symbols (half, quarter) are shown, multiply accordingly.
- Drawing a pictograph: (i) Choose a clear symbol; (ii) choose an appropriate scale so symbols are neither too many nor too few; (iii) draw whole symbols and, if needed, half/quarter symbols to show exact values; (iv) give a title, labels and the key.
- Use: Pictographs make it easier to compare categories quickly (good for simple data with small numbers).
- Limitations: Not good for very large or precise data, or when many different values are present.
How to read a pictograph
- Look at the key to find the value of one symbol.
- Count the symbols for the category.
- Multiply the number of symbols by the key to get the total value.
How to draw a pictograph from a table
- Choose a symbol (e.g., a small apple, star, car).
- Decide a convenient scale (1 symbol = 1, 2, 5, 10, etc.).
- For each category, divide the frequency by the scale to find the number of symbols to draw; draw whole symbols and if needed fractions (half symbol = half the scale).
- Write a clear key, title and labels for categories.
Tips for students
- Pick a scale that makes the number of symbols easy to draw (not too many tiny symbols).
- Always include the key and title so the pictograph is understandable by others.
- When using fractional symbols, make them clear (draw half-symbols clearly shaded or split).
- Example 1 — Reading a pictograph: A pictograph shows pets owned by students. Key: 1 dog symbol = 2 students. Dogs column has 4 dog symbols and 1 half-dog. Total students with dogs = (4 + 1/2) × 2 = 4.5 × 2 = 9 students.
- Example 2 — Drawing a pictograph: Data: Fruits sold in a shop in one day — Apples 30, Bananas 45, Oranges 15. Choose scale 1 symbol = 5 fruits. Number of symbols: Apples 30/5 = 6 symbols; Bananas 45/5 = 9 symbols; Oranges 15/5 = 3 symbols. Draw the chosen fruit symbol 6, 9 and 3 times respectively, give title and key '1 symbol = 5 fruits'.
- Example 3 — Using half symbols: School collected stationery items. Pens 23, Pencils 17. Choose scale 1 symbol = 5. Pens: 23/5 = 4 full symbols + 3/5 → draw 4 full symbols and one 3/5 symbol (or show fraction and write 23 beside it). Pencils: 17/5 = 3 full symbols + 2/5. Always mention the key to explain the fractions.
- Number of symbols = Frequency ÷ Scale (value of one symbol)
- Frequency = Number of symbols × Scale
- If using fractions: Frequency = (Full_symbols + Fractional_part) × Scale
Bar Graphs
What is a bar graph? A bar graph (or bar chart) is a way to present categorical data with rectangular bars. Each bar�s length (or height) is proportional to the value (frequency) of the category it represents. Bar graphs make it easy to compare quantities across different categories.
Key features:
- Axes: One axis (usually horizontal) lists categories; the other (usually vertical) shows the scale for frequency or amount.
- Bars: All bars have equal width and are spaced evenly; height (or length) shows the value.
- Title and labels: A clear title, and labels for both axes (including units) are needed.
- Scale: Choose a suitable scale so bars fit the graph area and are easy to read.
When to use: Use bar graphs for discrete or categorical data (e.g., favourite fruits, number of students in different clubs, daily sales by shop).
How to draw a bar graph (steps):
- Collect the data and list categories with their frequencies.
- Decide which axis will show categories and which will show frequency/amount.
- Choose a scale for the numerical axis so the largest value fits comfortably (for example, 1 small square = 2 units).
- Draw equal-width bars for each category; bar height = frequency (converted by the chosen scale).
- Give the graph a title, label axes, and include a key if needed (for coloured bars or multiple sets).
- Example 1 — Vertical bar graph (Books read by 5 students): Data: Asha 4, Ravi 7, Meera 5, Omar 3, Tina 6. Steps: (1) Horizontal axis: students (Asha, Ravi, Meera, Omar, Tina). Vertical axis: number of books (choose scale 1 square = 1 book up to 8). (2) Draw five equal-width bars; heights 4, 7, 5, 3, 6 respectively. (3) Title: 'Books read in a month'. Observe Ravi read the most (7) and Omar the least (3).
- Example 2 — Horizontal bar graph (Fruits sold in a day): Data: Apple 30, Banana 50, Mango 20, Orange 40. Steps: (1) Vertical axis: fruit names. Horizontal axis: number sold (choose scale 1 cm = 10 fruits or 1 square = 5 fruits). (2) Draw horizontal bars of length corresponding to each quantity. (3) Title: 'Fruits sold on Monday'. This layout is useful when category names are long.
- Example 3 — Double bar graph (Compare two classes): Data: Number of students who like Maths: Class 6A: {Like 12, Don't like 8}; Class 6B: {Like 9, Don't like 11}. Steps: (1) Use paired bars for each response ('Like', 'Don't like') with two colours (one for 6A, one for 6B). (2) Provide a legend. (3) Title: 'Interest in Maths: Class 6A vs 6B'. Interpretation: 6A has more students who like Maths than 6B.
- Frequency (f): the number of observations in a category (no special symbol needed).
- Total frequency (N) = sum of all frequencies = Σf.
- Range = Maximum value − Minimum value (useful to choose scale for numerical axis).
- Choosing scale (simple rule): scale ≈ (Highest frequency) / (Number of equal divisions on the axis). Then pick a convenient round number for the unit (e.g., 1, 2, 5, 10).
- Height (or length) of a bar = frequency × unit size (if you set 1 square = k units, height = frequency/k squares).
Interpreting and Comparing Data
What it means
Interpreting and comparing data means reading information presented in tables, pictographs and graphs, understanding what the numbers show, and drawing clear conclusions by comparing different groups or categories.
Why it is useful
- Helps to find which category is largest or smallest.
- Shows trends and patterns (increase, decrease, equal).
- Makes it easy to compare two or more sets of information quickly.
How to interpret a graph or table (step-by-step)
- Read the title to know what data is about.
- Look at the labels and units on the axes (for graphs) or the headings (for tables).
- Check the scale (how much each step on an axis or each symbol in a pictograph represents).
- Read the legend or key (for pictographs and some graphs) to know what symbols/colors mean.
- Note the values for each category and compare them: highest, lowest, similar values, or patterns over time.
- Use simple calculations (total, difference, percentage) when needed to make comparisons clearer.
Things to watch out for
- Different graphs may use different scales—always check the scale before comparing.
- Missing labels or unclear keys can change the meaning—ask for clarification.
- For comparisons over time, look for long-term trends, not just one point.
Short worked example inside the explanation
Suppose a pictograph shows the number of books read by groups of students: each book symbol (📘) = 2 books. The pictograph shows:
- A group: 📘📘📘 (3 symbols) → 3 × 2 = 6 books
- B group: 📘📘📘📘📘 (5 symbols) → 5 × 2 = 10 books
- C group: 📘📘 (2 symbols) → 2 × 2 = 4 books
- Example 1 — School activities: A table shows number of students in clubs: Sports 12, Music 8, Art 10, Science 15. Total students = 12+8+10+15 = 45. Which club has the most? Science (15). Difference between Science and Music = 15−8 = 7 students. Science percentage = (15/45)×100 = 33.33%.
- Example 2 — Pictograph: Each symbol ★ = 5 fruits sold in a week. Fruits sold: Apples ★★★ (15), Bananas ★★★★★ (25), Oranges ★★ (10). Compare: Bananas sold most, oranges least. Ratio of apples to oranges = 15:10 = 3:2.
- Example 3 — Bar graph (single): A vertical bar graph shows rainfall (mm) for five months: Jan 40, Feb 30, Mar 60, Apr 20, May 50. Interpret trend: rainfall rose from Feb to Mar, dropped in Apr, rose again in May. Highest month = March (60 mm), lowest = April (20 mm). Range = 60 − 20 = 40 mm.
- Example 4 — Double bar graph (comparing): Marks of two classes in Mathematics: Class A: 70, 82, 65, 90; Class B: 60, 88, 75, 85 (for four students). Use side-by-side bars to compare each student’s score. To find which class performed better overall calculate average (sum/number): Class A average = (70+82+65+90)/4 = 76.75, Class B average = (60+88+75+85)/4 = 77.0 → Class B slightly higher.
- Total frequency (N) = Sum of all frequencies (N = f1 + f2 + ... + fn)
- Percentage of a category = (category frequency / total frequency) × 100
- Relative frequency = category frequency ÷ total frequency
- Difference between two categories = larger value − smaller value
- Range = Maximum value − Minimum value (useful to compare spread)
- Mean (average, optional) = Sum of observations ÷ Number of observations
Choosing Representation
What it means
Choosing representation means deciding the best way to show collected data so that it is easy to read and understand. Different types of data and different purposes need different kinds of representations (tables, pictographs, bar graphs, line graphs, histograms, etc.).
How to decide
- Identify the type of data: categorical (names, colours, types) or numerical (counts, measurements).
- Decide the purpose: Do you want to compare categories, show change over time, or show parts of a whole?
- Check the size and range of data: Small counts suit pictographs, many values or wide ranges suit bar graphs or grouped forms (histograms).
- Simplicity and clarity: Choose a representation that is easy for the intended reader to understand.
Common choices
- Tally table or frequency table: Good for recording raw counts quickly.
- Pictograph (pictogram): Use when counts are small and a visual symbol helps (use a clear scale: e.g. 1 symbol = 2 items).
- Bar graph: Best for comparing different categories or groups (use equal-width bars with gaps between them).
- Line graph: Use for showing change over time (time on horizontal axis).
- Histogram: Use for grouped continuous numerical data (bars touch each other).
- Pie chart: Use to show parts of a whole (percentages) — use when you have a few categories.
Practical tips
- Always give a clear title, label axes, and include a scale or legend.
- Choose a scale with easy numbers (1, 2, 5, 10) so readers can read values quickly.
- Start the vertical axis at 0 when comparing sizes, to avoid misleading impressions.
- If numbers are large, group them (class intervals) to make drawing easier.
- Favourite fruits survey (30 students): use a pictograph if counts per fruit are small. Example: Apple = 8, Banana = 6, Mango = 10, Orange = 6. Use 1 fruit-symbol = 2 students.
- Number of books read by students: use a bar graph to compare number of books read by different students or houses.
- Monthly rainfall for 12 months: use a line graph to show change over time (months on x-axis, rainfall on y-axis).
- Marks of a large class grouped into intervals (0–10, 11–20, ...): use a histogram to show how many students fall in each interval.
- Market share of 4 brands: use a pie chart to show parts of the whole (convert counts to percentages).
- Frequency = number of occurrences of a value or category
- Relative frequency = Frequency / Total number of observations
- Percentage = (Frequency / Total) × 100
- Scale for pictograph: choose n so that 1 symbol = n items. Example: if max count = 24 and you want at most 12 symbols, choose n = 2.
- Class width (for grouped data) ≈ (Max value − Min value) / Number of classes (round to a convenient number)
Key Concepts
- Data
- Facts, numbers or measurements collected for analysis.
- Raw data
- Unorganized original data as collected before any processing.
- Observation
- A single data value or measurement in a data set.
- Variable
- A characteristic or quantity that can take different values.
- Frequency
- Number of times a particular value or class occurs in the data.
- Tally marks
- A quick method of counting using groups of five strokes (||||/).
- Ungrouped data
- Data listed individually without grouping into intervals.
- Grouped data
- Data organized into class intervals with frequencies for each interval.
- Class interval
- A range of values combined into one group in grouped data.
- Class width
- Difference between the upper and lower limits of a class (upper − lower).
- Frequency distribution
- A table showing values or class intervals with their corresponding frequencies.
- Pictograph (Pictogram)
- A chart that uses pictures or symbols to represent data; each symbol stands for a fixed number.
- Bar graph
- A graph using bars of equal width to show frequencies of different categories.
- Histogram
- A bar-like graph for grouped continuous data with adjacent (touching) bars where heights show frequencies.
- Frequency polygon
- A line graph formed by joining points plotted at class midpoints and their frequencies.
- Cumulative frequency
- The running total of frequencies up to and including a given value or class.
- Mode
- The value(s) that occur most frequently in a data set.
- Median
- The middle value when data are arranged in order; if there is an even number, it is the average of the two middle values.
- Mean (Arithmetic mean)
- Sum of all observations divided by the number of observations.
- Range
- Difference between the maximum and minimum values in a data set.
End-of-Chapter Trial Paper & Test Questions
Topic-wise questions to test your understanding of every concept in this chapter.
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In a tally chart, the mark ||||/ represents: / एक टैली चार्ट में ||||/ दर्शाता है: (a) 4 / 4 (b) 5 / 5 (c) 6 / 6 (d) 10 / 10
Show answer
(b) 5 / 5 — In tally marks, four vertical strokes are made and the fifth observation is recorded by drawing a diagonal across the previous four (||||/), making a group of five. / टैली चिह्नों में चार लंबी रेखाएँ खींची जाती हैं और पाँचवाँ प्रेक्षण उनके आर-पार तिरछी रेखा (||||/) खींचकर दर्शाया जाता है, जो पाँच का समूह बनाता है।
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A bar graph for favourite fruits of 30 students shows Mango: 12, Apple: 8, Banana: 6, Orange: 4. Which fruit is most popular? / 30 छात्रों के पसंदीदा फल का बार ग्राफ दिखाता है: आम: 12, सेब: 8, केला: 6, संतरा: 4। कौन-सा फल सबसे लोकप्रिय है? (a) Apple / सेब (b) Banana / केला (c) Mango / आम (d) Orange / संतरा
Show answer
(c) Mango / आम — The bar for Mango has the highest frequency (12 students), which means its bar in the bar graph is the tallest. / आम का बार सबसे अधिक आवृत्ति (12 छात्र) दर्शाता है, जिसका अर्थ है बार ग्राफ में उसकी पट्टी सबसे ऊँची है।
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In a pictograph, each symbol represents 5 students. If the row for 'Hockey' shows 3 full symbols and 1 half symbol, how many students like Hockey? / एक चित्रालेख में प्रत्येक प्रतीक 5 छात्रों को दर्शाता है। यदि 'हॉकी' की पंक्ति में 3 पूर्ण और 1 आधा प्रतीक है, तो हॉकी पसंद करने वाले कितने छात्र हैं? (a) 15 / 15 (b) 17 / 17 (c) 17.5 / 17.5 (d) 20 / 20
Show answer
(c) 17.5 / 17.5 — Number of students = (3 + 0.5) × 5 = 3.5 × 5 = 17.5. / छात्रों की संख्या = (3 + 0.5) × 5 = 3.5 × 5 = 17.5।
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In a data set, frequency means ______. / डेटा समूह में आवृत्ति (frequency) का अर्थ ______ है।
Show answer
The number of times a particular value or category occurs in the data / किसी विशेष मान या श्रेणी का डेटा में कितनी बार आना — Frequency is the count of how many times each observation or category appears. It is the basic measure in a frequency table. / आवृत्ति प्रत्येक प्रेक्षण या श्रेणी के आने की संख्या है। यह आवृत्ति तालिका का आधारभूत माप है।
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The range of the data set {29, 33, 31, 27, 35} is ______. / डेटा समूह {29, 33, 31, 27, 35} का परिसर ______ है।
Show answer
8 / 8 — Range = Maximum value − Minimum value = 35 − 27 = 8. / परिसर = अधिकतम मान − न्यूनतम मान = 35 − 27 = 8।
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True or False: In a bar graph, all bars should have the same width and equal gaps between them. / सत्य या असत्य: बार ग्राफ में सभी पट्टियों की चौड़ाई समान होनी चाहिए और उनके बीच बराबर अंतर होना चाहिए।
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True / सत्य — In a standard bar graph, equal-width bars with equal spacing allow fair visual comparison of the frequencies of different categories. / मानक बार ग्राफ में समान चौड़ाई की पट्टियाँ और बराबर अंतर विभिन्न श्रेणियों की आवृत्तियों की उचित दृश्य तुलना सुनिश्चित करता है।
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A survey records books read per month by 6 students: 3, 5, 2, 5, 4, 5. What is the mode? / 6 छात्रों द्वारा प्रति माह पढ़ी गई पुस्तकों का सर्वेक्षण: 3, 5, 2, 5, 4, 5। बहुलक (mode) क्या है?
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5 / 5 — The mode is the value that appears most frequently. 5 appears 3 times (more than any other value), so mode = 5. / बहुलक वह मान है जो सबसे अधिक बार आता है। 5 तीन बार आता है (किसी अन्य से अधिक), अतः बहुलक = 5।
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A pictograph shows the number of cars sold in 4 days (each car symbol = 10 cars). Monday: 3 symbols, Tuesday: 5 symbols, Wednesday: 2 symbols, Thursday: 4 symbols. How many more cars were sold on Tuesday than on Wednesday? / एक चित्रालेख 4 दिन की कार बिक्री दिखाता है (प्रत्येक प्रतीक = 10 कारें)। सोमवार: 3, मंगलवार: 5, बुधवार: 2, गुरुवार: 4 प्रतीक। मंगलवार को बुधवार से कितनी अधिक कारें बिकीं?
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30 cars / 30 कारें — Tuesday: 5 × 10 = 50 cars. Wednesday: 2 × 10 = 20 cars. Difference: 50 − 20 = 30 cars. / मंगलवार: 5 × 10 = 50 कारें। बुधवार: 2 × 10 = 20 कारें। अंतर: 50 − 20 = 30 कारें।
Related Laws & Principles
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