Question 1

The marks obtained by 5 students in Mathematics are: 10, 15, 12, 15, 18. What is the mean of these marks?

Accepted Answer

Mean = (10 + 15 + 12 + 15 + 18) ÷ 5 = 70 ÷ 5 = 14.

Question 2

The heights (in cm) of 7 children are: 120, 125, 120, 130, 128, 125, 122. What is the median height?

Accepted Answer

Arranging in order: 120, 120, 122, 125, 125, 128, 130; the middle (4th) value is 125.

Question 3

In a survey, the number of family members in 8 households are: 4, 5, 4, 6, 5, 4, 7, 5. What is the mode?

Accepted Answer

The mode is the value that appears most frequently; 5 appears 3 times, which is more than any other value.

Question 4

The variance of the dataset {2, 4, 6, 8, 10} is:

Accepted Answer

Mean = 6; variance = [(2-6)² + (4-6)² + (6-6)² + (8-6)² + (10-6)²]/5 = (16+4+0+4+16)/5 = 40/5 = 8.

Question 5

If the standard deviation of a set of numbers is 5, what is the variance?

Accepted Answer

Variance is the square of standard deviation; Variance = SD² = 5² = 25.

Question 6

The variance of {5, 5, 5, 5, 5} is:

Accepted Answer

When all values are identical, the mean equals each value, so all deviations are zero and variance = 0.

Question 7

A bag contains 5 red balls and 3 blue balls. If one ball is drawn at random, what is the probability that it is red?

Accepted Answer

Probability = (Number of red balls) / (Total number of balls) = 5 / (5 + 3) = 5/8.

Question 8

A fair die is rolled once. What is the probability of getting a number greater than 4?

Accepted Answer

Numbers greater than 4 on a die are 5 and 6, so favorable outcomes = 2 and total outcomes = 6; probability = 2/6.

Question 9

Two fair coins are tossed together. What is the probability of getting at least one head?

Accepted Answer

Possible outcomes: HH, HT, TH, TT (total = 4); favorable outcomes with at least one head: HH, HT, TH (count = 3); probability = 3/4.

Question 10

In how many ways can 5 different books be arranged on a shelf?

Accepted Answer

Number of permutations of 5 distinct objects = 5! = 5 × 4 × 3 × 2 × 1 = 120.

Question 11

How many ways can a committee of 3 people be selected from a group of 7 people?

Accepted Answer

Number of combinations = C(7,3) = 7!/(3! × 4!) = (7 × 6 × 5)/(3 × 2 × 1) = 35.

Question 12

A student must answer 4 questions out of 6 questions in an exam. In how many ways can the student select the questions?

Accepted Answer

Number of combinations = C(6,4) = 6!/(4! × 2!) = (6 × 5)/(2 × 1) = 15.

Question 13

The marks obtained by 5 students in a test are: 10, 20, 30, 40, 50. What is the variance of these marks?

Accepted Answer

Mean = 30; Variance = [(10-30)² + (20-30)² + (30-30)² + (40-30)² + (50-30)²]/5 = [400+100+0+100+400]/5 = 1000/5 = 200.

Question 14

Two datasets have standard deviations of 5 and 10 respectively. Which dataset has greater variability?

Accepted Answer

Standard deviation measures spread; a larger standard deviation (10) indicates greater variability than a smaller one (5).

Question 15

The variance of the dataset 6, 6, 6, 6, 6 is:

Accepted Answer

When all values are identical, the mean equals each value, so all deviations are zero, making variance = 0.

Question 16

The daily temperatures (in °C) for a week are: 22, 24, 22, 26, 28, 22, 25. Which measure of central tendency is 22?

Accepted Answer

22 appears 3 times (most frequent), making it the mode; the mean is 23.57 and median is 24 (neither equals 22).

Question 17

How many 4-digit numbers can be formed using the digits 2, 3, 5, 7 without repetition?

Accepted Answer

All 4 digits must be used in different positions, which is a permutation: P(4,4) = 4! = 24.

Question 18

From 6 officers, 2 must be chosen for night patrol duty. In how many ways can they be selected?

Accepted Answer

Since the order of selection does not matter (both patrol together), use combination: C(6,2) = 6!/(2! × 4!) = (6 × 5)/2 = 15.

Question 19

If the standard deviation of a dataset is 8, what is the variance?

Accepted Answer

Variance is the square of standard deviation; Variance = (8)² = 64.

Question 20

In how many ways can 5 students be arranged in a line for a photograph?

Accepted Answer

This is a permutation problem where all 5 students must be arranged in order: 5! = 5 × 4 × 3 × 2 × 1 = 120.

Agniveer Army CEE Statistics Questions

Statistics Practice Questions — Graded Difficulty