CBSE Class 7 Maths Exemplar Chapter 3: Data Handling NCERT Solutions

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This resource provides detailed NCERT Solutions for CBSE Class 7 Maths Exemplar, Chapter 3: Data Handling. It covers fundamental concepts of statistics, including how to calculate the mean, median, and mode of a dataset. The solutions explain how to find the range of data and identify which measure of central tendency is most appropriate for different scenarios. It also addresses how extreme values affect these measures. These solutions are designed to help students understand the core principles of data handling, solve practice problems effectively, and prepare thoroughly for their examinations by clarifying each step and concept.

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BoardCBSE
ClassClass 7
SubjectMaths Exemplar
Session2026
LanguageEnglish
TypeNCERT Solutions
ChapterChapter 3

Chapter summary

Chapter 3 of the CBSE Class 7 Maths Exemplar focuses on Data Handling. This section provides NCERT Solutions that explain key statistical measures: mean, median, mode, and range. Students will learn to calculate these measures for given datasets and understand their significance. The solutions also explore the impact of extreme values on these central tendencies and guide students in selecting the most appropriate measure for various data-related problems.

Learning outcomes

  • Understand the definition and calculation of mean for a set of observations.
  • Identify and calculate the mode of a given dataset.
  • Determine the median of a dataset by arranging it in order.
  • Calculate the range of a dataset by finding the difference between the highest and lowest values.
  • Analyze the effect of extreme values on mean, median, and mode.
  • Select the appropriate measure of central tendency for a given data scenario.

Topics covered

Paper topics

  • Mean
  • Median
  • Mode
  • Range
  • Measures of Central Tendency
  • Data Interpretation
  • Data Organization
  • Central Tendency Affected by Extreme Values

Important topics

  • Calculating Mean
  • Finding Median
  • Determining Mode
  • Understanding Range
  • Choosing the Right Measure of Central Tendency

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Questions and Solutions

Question 1

Let x, y, and z be three observations. What is the mean of these observations?
Solution: The mean of a set of observations is calculated by summing all the observations and then dividing by the total number of observations. For the given three observations x, y, and z, the sum is \(x + y + z\). The number of observations is 3. Therefore, the mean is \(\frac{x + y + z}{3}\).

The correct option is (b).

Question 2

The number of trees in different parks of a city are 33, 38, 48, 33, 34, 34, 33 and 24. What is the mode of this data?
Solution: The mode of a dataset is the value that appears most frequently. Let's count the occurrences of each number:
  • 24: occurs 1 time
  • 33: occurs 3 times
  • 34: occurs 2 times
  • 38: occurs 1 time
  • 48: occurs 1 time
The number 33 appears most frequently (3 times). Therefore, the mode of this data is 33.

The correct option is (c).

Question 3

Which measures of central tendency get affected if the extreme observations on both the ends of a data arranged in descending order are removed?
Solution: Let's consider the measures of central tendency:
  • Mean: The mean is calculated by summing all observations and dividing by the count. Removing extreme values will change the sum and potentially the count, thus significantly affecting the mean.
  • Median: The median is the middle value when the data is arranged in order. If extreme values are removed from both ends, the middle value might shift, affecting the median.
  • Mode: The mode is the most frequent observation. Removing extreme values, which usually occur less frequently, is unlikely to change the mode unless those extreme values were the modes themselves.
Therefore, the mean and median are affected when extreme observations are removed from both ends of the data.

The correct option is (b).

Question 4

What is the range of the data: 21, 6, 17, 18, 12, 8, 4, 13?
Solution: The range of a dataset is the difference between the highest and the lowest observation. First, identify the highest and lowest values in the given data: 21, 6, 17, 18, 12, 8, 4, 13. The highest observation is 21. The lowest observation is 4. The range is calculated as: Range = Highest observation - Lowest observation. Range = \(21 - 4\) = \(17\).

The correct option is (a).

Question 5

What is the median of the data: 3, 4, 5, 6, 3, 4, 7?
Solution: To find the median, we first need to arrange the data in ascending (or descending) order. The given data is: 3, 4, 5, 6, 3, 4, 7. Arranging the data in ascending order, we get: 3, 3, 4, 4, 5, 6, 7. There are 7 observations in total. The median is the middle observation. In a dataset with an odd number of observations, the median is the \(\frac{(n+1)}{2}\)th observation, where n is the number of observations. Here, n = 7, so the median is the \(\frac{(7+1)}{2}\) = \(\frac{8}{2}\) = 4th observation. The 4th observation in the ordered list (3, 3, 4, 4, 5, 6, 7) is 4. Therefore, the median of the data is 4.

The correct option is (c).

Question 6

Out of 5 brands of chocolates in a shop, a boy has to purchase the brand which is most liked by children. What measure of central tendency would be most appropriate if the data is provided to him?
Solution: The boy wants to choose the brand that is most liked by children. This means he is looking for the brand that appears most frequently in the data collected about children's preferences. The measure of central tendency that represents the most frequent value in a dataset is the mode. Therefore, the mode would be the most appropriate measure to help him make his decision.

The correct option is (b).

Question 7

There are 2 aces in each of the given set of cards placed face down. From which set are you certain to pick the two aces in the first go?
Solution: Certainty in picking the two aces in the first go implies that there are only two cards, and both are aces. Let's analyze the options based on the description:
  • (a) This set likely contains more than two cards, making it uncertain to pick both aces in the first go.
  • (b) This set also likely contains more than two cards.
  • (c) This set is described as having only two cards placed face down. If these two cards are the two aces, then picking them in the first go is certain.
  • (d) This set likely contains more than two cards.
Therefore, you are certain to pick the two aces in the first go from the set that contains only those two aces.

The correct option is (c).

Common mistakes

  • Confusing the formulas for mean, median, and mode.
  • Incorrectly identifying the most frequent observation for the mode.
  • Errors in arranging data in ascending or descending order to find the median.
  • Calculating the range incorrectly by not using the absolute highest and lowest values.
  • Misunderstanding how extreme values influence different measures of central tendency.

Revision tips

  • Practice calculating mean, median, and mode for various datasets.
  • Pay close attention to the definition and application of each measure of central tendency.
  • Understand how to arrange data correctly to find the median.
  • Review the impact of outliers on the mean, median, and mode.
  • Work through the examples to solidify your understanding of range calculation.

Practice MCQs

Q1. What is the mean of three observations x, y, and z?

Q2. What is the mode of the data: 33, 38, 48, 33, 34, 34, 33, 24?

Q3. Which measures of central tendency are affected if the extreme observations on both ends of a data arranged in descending order are removed?

Q4. What is the range of the data: 21, 6, 17, 18, 12, 8, 4, 13?

Q5. What is the median of the data: 3, 4, 5, 6, 3, 4, 7?

Q6. If a boy needs to choose the most liked brand of chocolates among children, which measure of central tendency is most appropriate?

Frequently asked questions

What is the main focus of CBSE Class 7 Maths Exemplar Chapter 3?

Chapter 3, Data Handling, focuses on understanding and calculating key statistical measures like mean, median, mode, and range for datasets.

How are the NCERT Solutions for this chapter helpful?

These solutions provide clear, step-by-step explanations for each problem, helping students grasp concepts like data organization, central tendencies, and the impact of extreme values, aiding in exam preparation.

What is the difference between mean, median, and mode?

The mean is the average, calculated by summing all values and dividing by the count. The median is the middle value when data is ordered. The mode is the value that appears most frequently.

How do extreme values affect the measures of central tendency?

Extreme values (outliers) significantly affect the mean by pulling it towards them. They have a lesser impact on the median and usually no impact on the mode unless the extreme value itself is the mode.

What is the range of a dataset?

The range is the difference between the highest and the lowest value in a dataset, providing a simple measure of the data's spread.

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