Are these practice questions for Statistics based on the CBSE pattern?

Yes. Every practice question is modeled on the CBSE Class 11 - Science Mathematics exam pattern — including MCQs, assertion-reason questions, and short-answer formats that frequently appear in CBSE papers.

Are the practice questions for Statistics free?

Yes. Every chapter includes free practice questions for Class 11 - Science students to get you started.

What types of questions are included?

The practice set for Statistics mainly includes MCQs and CBSE-style short-answer questions, with instant feedback on each answer. For full-length textbook practice, use the NCERT Solutions page.

Are the practice questions suitable for board exam preparation?

Yes. The questions test the same concepts and depth that CBSE asks in board exams. After finishing, also solve the NCERT and NCERT Exemplar exercises for Statistics for full coverage.

How many practice questions are there for Statistics?

The number scales with chapter length and concept density. Each chapter typically has 15-50 practice questions across MCQ and short-answer formats.

Statistics Class 11 Mathematics Practice Questions with Answers

easy

Explain what is meant by a 'discrete frequency distribution' and a 'continuous frequency distribution'.

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easy

The sum of squares of deviations for

10

observations taken from their mean

50

is

250

. Calculate the variance.

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easy

Name the four measures of dispersion mentioned in your chapter.

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easy

Calculate the range for the following set of observations:

18, 25, 12, 45, 21, 52, 19, 33

.

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easy

Justify why the sum of deviations of a set of observations from their arithmetic mean is always zero, and explain why this property makes it an unsuitable basis for a measure of dispersion.

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easy

What is the relationship between Variance and Standard Deviation?

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easy

Define 'Range' as a measure of dispersion.

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easy

Two batsmen have the same average score of 55 runs. The standard deviation of scores for Batsman A is 8 runs, while for Batsman B it is 20 runs. Evaluate which batsman is a more dependable choice for a team and justify your answer.

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easy

State the formula for the variance (

\sigma^2

) of ungrouped data with

n

observations

x_1, x_2, \ldots, x_n

and mean

\bar{x}

.

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easy

If the variance of a data set is

64

, calculate its standard deviation.

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easy

Explain why the sum of absolute deviations is taken when calculating mean deviation, instead of the sum of the deviations themselves.

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medium

Explain why the sum of squares of deviations from the mean,

\sum_{i=1}^{n}\left(x_{i}-\bar{x}\right)^{2}

, is not considered a proper measure of dispersion on its own, and how 'variance' overcomes this issue.

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medium

Summarize the procedure for finding the median of a continuous frequency distribution.

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medium

Calculate the mean and variance for the following continuous frequency distribution:

Class Interval	0-10	10-20	20-30	30-40	40-50
Frequency	5	8	15	16	6

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medium

Create a dataset of 5 distinct integers such that its mean is 8 and its range is 10. Then, calculate the mean deviation about the mean for the dataset you created.

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medium

A student claims that if the range of a dataset is zero, its standard deviation must also be zero. Critique this statement. Is it always true? Justify your reasoning.

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medium

Calculate the variance and standard deviation for the data:

5, 8, 10, 12, 15

.

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medium

Calculate the mean deviation about the mean for the following frequency distribution:

$x_i$	10	20	30	40	50
$f_i$	4	5	8	2	1

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medium

Calculate the mean deviation about the mean for the first five prime numbers.

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medium

A teacher has the marks of two students, Alex and Ben, from 5 tests: Alex: 85, 90, 82, 88, 95 Ben: 95, 92, 98, 60, 95 The teacher wants to award the "Most Consistent Performer" prize. Propose a statistical method to determine the winner. Justify your choice of method and use it to decide who should get the prize.

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medium

Formulate a dataset of four distinct positive integers whose arithmetic mean is 10 and whose median is 9.

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medium

Calculate the mean deviation about the median for the following data:

15, 22, 18, 25, 12, 10

.

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medium

Describe in detail the steps to calculate the mean deviation about the median for ungrouped data, considering both cases where the number of observations is even and odd.

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medium

Analyze the effect on the variance of a data set if each observation is decreased by

10

.

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medium

Describe the primary difference between a measure of central tendency and a measure of dispersion. Use the example of the two batsmen A and B from the source text to illustrate.

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medium

Using the shortcut method, calculate the mean and standard deviation for the following distribution:

Height (cm)	120-130	130-140	140-150	150-160	160-170
No. of Students	2	8	12	10	8

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medium

Recall the value of the sum of deviations of a set of observations from their arithmetic mean.

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medium

The mean salary in Company A is ₹60,000 with a standard deviation of ₹6,000. In Company B, the mean salary is ₹75,000 with a standard deviation of ₹9,000. Evaluate which company has a more uniform salary structure and justify your answer.

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medium

Formulate a rigorous algebraic proof to show that variance is independent of the change of origin. That is, if a new set of observations

y_i

is created by adding a constant 'a' to each observation

x_i

(i.e.,

y_i = x_i + a

), prove that the variance of

y

is equal to the variance of

x

.

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medium

The sum of the squares of the deviations of a set of 10 observations from their mean of 20 is 250. Justify that the standard deviation is 5. Now, if each observation is increased by 5, justify how the new standard deviation is affected.

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medium

Identify the formula for calculating the mean of a discrete frequency distribution with

n

distinct values

x_1, x_2, \ldots, x_n

occurring with frequencies

f_1, f_2, \ldots, f_n

. Explain each term in the formula.

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medium

List the steps required to calculate the mean deviation about the mean for a discrete frequency distribution.

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hard

Derive the shortcut formula for variance,

\sigma^2 = \frac{h^2}{N^2} [N \sum f_i y_i^2 - (\sum f_i y_i)^2]

, where

y_i = \frac{x_i - A}{h}

. Justify each step of the derivation starting from the basic definition of variance,

\sigma_x^2 = \frac{1}{N} \sum f_i (x_i - \bar{x})^2

.

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hard

Design a discrete frequency distribution with at least 4 distinct values (

x_i

) and a total frequency (

N

) of 20, such that the mean of the distribution is exactly 10.

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hard

If a constant value 'a' is added to each observation in a data set, what is the effect on the variance? Explain why.

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hard

The scores of two batsmen, P and Q, in five innings are given below. Analyze their scores to determine who is the more consistent player. Batsman P:

25, 50, 45, 30, 70

Batsman Q:

40, 48, 50, 52, 55

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hard

The variance of a set of observations is 25. If each observation is multiplied by -3, justify what the new variance will be without performing detailed calculations.

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hard

A researcher analyzed the dataset {5, 10, 15, 20, 200} and concluded that since the mean deviation about the mean is relatively small compared to the maximum value, the data has low dispersion. Critique this conclusion. Propose a more appropriate measure of central tendency and dispersion for this specific dataset and justify your choice.

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hard

The mean and standard deviation of 50 observations were calculated as 60 and 5 respectively. It was later discovered that one observation, 75, was misread as 25. Calculate the correct mean and correct standard deviation.

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hard

Calculate the mean deviation about the median for the following data:

Class	0-10	10-20	20-30	30-40	40-50	50-60
Frequency	6	8	14	16	4	2

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hard

Create two different sets of data, A and B, each with 5 data points. Both sets must have the same mean of 20 and the same range of 16. Then, calculate the standard deviation for both sets. Evaluate which dataset is more dispersed and justify why the range can be a misleading measure of dispersion.

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hard

The mean of 5 observations is

6

and the variance is

6.8

. If three of the observations are

2, 4,

and

8

, find the other two observations.

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hard

The mean and standard deviation of 100 observations were calculated as 20 and 3, respectively. It was later discovered that three observations, 21, 21, and 18, were incorrect. If these incorrect observations are removed from the data, critique the expected impact and then formulate the steps to calculate the new mean and new standard deviation for the remaining 97 observations.

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hard

Two distributions have the same mean. The first distribution has

10

observations with a standard deviation of

3

, and the second has

15

observations with a standard deviation of

2

. If the observations are combined, will the standard deviation of the combined group be less than, equal to, or greater than the average of the two standard deviations? Justify your answer without calculation.

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hard

Explain the shortcut method for calculating variance for a continuous frequency distribution. Define each term used in the formula

\sigma^{2}=\frac{h^{2}}{\mathrm{~N}^{2}}\left[\mathrm{~N} \sum f_{i} y_{i}^{2}-\left(\sum f_{i} y_{i}\right)^{2}\right]

.

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StatisticsClass 11 Mathematics Practice Questions