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Chapter 4 · Class 7 Mathematics

Data Handling — Important Questions

25 questions With answers CBSE format

SUMMARY: The chapter "Data Handling" introduces students to the concepts of organizing, representing, and interpreting data.
KEY TOPICS: data collection, bar graphs, double bar graphs, organizing data, mean, median, mode, probability, pie charts, interpreting data

Previous chapter Congruence of Triangles Next chapter Exponents and Powers

Multiple Choice Questions (MCQs) 5 questions

Q1 1 Mark

What is the mode of the following data set: 3, 7, 3, 2, 5, 3, 8?

A3

B5

C2

D7

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Correct answer: Option 1 — 3

Q2 1 Mark

Which of the following is a measure of central tendency?

ARange

BMean

CFrequency

DOutlier

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Correct answer: Option 2 — Mean

Q3 1 Mark

If the mean of the numbers 4, 8, x, and 12 is 10, what is the value of x?

A10

B12

C16

D8

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Correct answer: Option 1 — 10

Q4 1 Mark

In a survey of 100 students, 30 liked Mathematics, 50 liked Science, and 20 liked both. What is the probability that a student chosen at random likes only Mathematics?

A0.3

B0.2

C0.1

D0.5

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Correct answer: Option 2 — 0.2

Q5 1 Mark

A class has 40 students. The heights of the students are recorded. If the heights are normally distributed, which of the following statements is true?

AMost students have heights near the average.

BAll students have the same height.

CHeights are uniformly distributed.

DThere are no variations in heights.

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Correct answer: Option 1 — Most students have heights near the average.

Short Answer Questions 5 questions

Q6 3 Marks

What is the difference between a bar graph and a histogram?

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A bar graph represents categorical data with rectangular bars, where the length of each bar is proportional to the value it represents. A histogram, on the other hand, is used for continuous data and shows the frequency distribution of numerical data using adjacent bars without gaps.

Q7 3 Marks

Define mean, median, and mode in the context of a data set. Provide an example for each.

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The mean is the average of a data set, calculated by summing all values and dividing by the number of values. The median is the middle value when the data is arranged in order. The mode is the value that appears most frequently. For example, in the data set {2, 3, 3, 5, 7}, the mean is 4, the median is 3, and the mode is 3.

Q8 3 Marks

How do you calculate the range of a data set?

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The range of a data set is calculated by subtracting the smallest value from the largest value. For example, in the data set {4, 8, 15, 16, 23}, the range is 23 - 4 = 19.

Q9 3 Marks

Explain how to create a frequency table from a given data set.

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To create a frequency table, first list all unique values from the data set. Then, count how many times each value appears and record these counts next to the corresponding values. This table helps in visualizing the distribution of data.

Q10 3 Marks

What is a pie chart, and how is it different from a bar graph?

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A pie chart is a circular statistical graphic divided into slices to illustrate numerical proportions, where each slice represents a category's contribution to the whole. Unlike a bar graph, which uses bars to compare different categories, a pie chart shows the relative sizes of parts to a whole, making it easier to visualize percentage distribution.

Long Answer Questions 5 questions

Q11 6 Marks

Explain the concept of mean, median, and mode in data handling. Provide an example for each and illustrate how they can be used to analyze a set of data.

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Mean is the average of a set of numbers, calculated by adding all the values and dividing by the count of values. For example, for the data set {2, 4, 6, 8}, the mean is (2+4+6+8)/4 = 5. Median is the middle value when the data is arranged in ascending order. For the same data set, the median is 5, as it is the average of the two middle numbers (4 and 6). Mode is the value that appears most frequently in a data set. In the data set {1, 2, 2, 3, 4}, the mode is 2. These measures help summarize and understand the distribution of data, revealing trends and patterns.

Q12 6 Marks

A teacher recorded the marks obtained by students in a mathematics test. The marks are as follows: 45, 56, 67, 45, 78, 89, 67, 45, 90. Calculate the mean, median, and mode of the marks. Explain the significance of each measure in understanding the students' performance.

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To calculate the mean, add all the marks: 45 + 56 + 67 + 45 + 78 + 89 + 67 + 45 + 90 = 522. The mean is 522/9 = 58. The median is the middle value when arranged in order: {45, 45, 45, 56, 67, 67, 78, 89, 90}, which gives a median of 67. The mode is 45, as it appears most frequently. The mean provides an overall average performance, the median indicates the central tendency, and the mode highlights the most common score, helping the teacher identify areas where students excel or struggle.

Q13 6 Marks

Discuss the importance of data representation through bar graphs and pie charts. Create a bar graph and a pie chart using the following data: Favorite fruits of students - Apples: 10, Bananas: 15, Oranges: 5, Grapes: 8. Explain how these visual tools can enhance the understanding of data.

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Bar graphs represent data using rectangular bars, where the length of each bar is proportional to the value it represents. In this case, the bar graph would show the number of students preferring each fruit, making it easy to compare the popularity of each fruit visually. Pie charts represent data as a whole, divided into slices that show the proportion of each category. For the given data, the pie chart would illustrate the percentage of students who prefer each fruit, providing a clear visual of preferences. These visual tools enhance understanding by simplifying complex data into easily interpretable formats, aiding in quick analysis and decision-making.

Q14 6 Marks

A survey was conducted to find out the number of books read by students in a month. The results are as follows: 0, 1, 2, 2, 3, 3, 3, 4, 5, 5, 5, 6. Calculate the range, variance, and standard deviation of the data. Discuss how these measures can help in understanding the variability in the data.

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To calculate the range, subtract the smallest value from the largest: 6 - 0 = 6. Variance is calculated by finding the average of the squared differences from the mean. The mean is 3, so the squared differences are: (0-3)², (1-3)², (2-3)², etc. The variance is the average of these squared differences. The standard deviation is the square root of the variance. These measures help in understanding the variability in the data; a higher variance or standard deviation indicates greater spread in the number of books read, while a lower value suggests that most students read a similar number of books.

Q15 6 Marks

Imagine you are conducting a research project on the daily screen time of students. You collected the following data: 1, 2, 3, 4, 5, 5, 6, 7, 8, 9. Analyze this data by calculating the mean, median, mode, and range. Discuss how these statistics can inform decisions regarding screen time management for students.

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To find the mean, add all values: 1 + 2 + 3 + 4 + 5 + 5 + 6 + 7 + 8 + 9 = 50, and divide by 10 to get a mean of 5.5. The median, being the middle value in the ordered set {1, 2, 3, 4, 5, 5, 6, 7, 8, 9}, is 5.5. The mode is 5, as it appears most frequently. The range is 9 - 1 = 8. These statistics provide insights into the average screen time, the typical experience of students, and the spread of data, which can guide parents and educators in setting appropriate screen time limits to promote healthier habits.

Assertion–Reason Questions 5 questions

Q16 1 Mark

Assertion (A): The mode of a set of data is the value that appears most frequently.

Reason (R): The mode is always one of the values in the data set.

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Correct answer: Option 1 — Both A and R are true, and R is the correct explanation of A.

Q17 1 Mark

Assertion (A): A bar graph can represent both discrete and continuous data.

Reason (R): Bar graphs are used only for discrete data.

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Correct answer: Option 3 — A is true, but R is false.

Q18 1 Mark

Assertion (A): The median of a data set is the middle value when the data is arranged in order.

Reason (R): The median is always affected by extreme values in the data set.

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Correct answer: Option 4 — A is false, but R is true.

Q19 1 Mark

Assertion (A): A pie chart can effectively show the relative proportions of different categories in a data set.

Reason (R): Pie charts are not suitable for comparing more than three categories.

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Correct answer: Option 3 — A is true, but R is false.

Q20 1 Mark

Assertion (A): The range of a data set is calculated by subtracting the smallest value from the largest value.

Reason (R): The range provides a measure of how spread out the values are in the data set.

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Correct answer: Option 1 — Both A and R are true, and R is the correct explanation of A.

Statement-Based Questions 5 questions

Q21 1 Mark

Statement 1: The mode of a set of numbers is the number that appears most frequently.

Statement 2: The median is the average of the highest and lowest values in a data set.

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Correct answer: Option 1 — Both statements are true.

Q22 1 Mark

Statement 1: A bar graph can represent categorical data.

Statement 2: A pie chart is used for displaying continuous data.

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Correct answer: Option 3 — Only Statement 2 is true.

Q23 1 Mark

Statement 1: The range of a data set is calculated by subtracting the smallest value from the largest value.

Statement 2: The mean is always greater than the median in a data set.

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Correct answer: Option 2 — Only Statement 1 is true.

Q24 1 Mark

Statement 1: A histogram can show the frequency of data within certain intervals.

Statement 2: The mode can be found by arranging the data in ascending order.

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Correct answer: Option 4 — Both statements are false.

Q25 1 Mark

Statement 1: Data can be represented using tables, graphs, and charts.

Statement 2: The median is always the middle value in a data set when arranged in order.

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Correct answer: Option 1 — Both statements are true.

Previous chapter Congruence of Triangles Next chapter Exponents and Powers

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