Elementary Statistics MCQ Quiz - Objective Question with Answer for Elementary Statistics - Download Free PDF

Last updated on Jul 17, 2025

Testbook has brought to you some of the most popular Elementary Statistics MCQ Quiz to practice and ace for the exam. These syllabus- specific Elementary Statistics Question Answers will help candidates in their upcoming interviews and competitive exams such as UPSC, NDA, Insurance exams, Law exams and even graduate exams. Candidates can attempt these Elementary Statistics Objective Questions that are provided with detailed solutions for you to peruse and learn from.

Latest Elementary Statistics MCQ Objective Questions

Elementary Statistics Question 1:

The mean and the mode of a data set are 51.5 and 61.7, respectively. Find the median of the data set, using the empirical formula.

  1. 55.4
  2.  54.9
  3.  56.1
  4.  54.3

Answer (Detailed Solution Below)

Option 2 :  54.9

Elementary Statistics Question 1 Detailed Solution

Given:

Mean (M) = 51.5

Mode (Mo) = 61.7

Formula used:

Median = M + (Mo - M) / 3

Calculation:

⇒ Median = 51.5 + (61.7 - 51.5) / 3

⇒ Median = 51.5 + 10.2 / 3

⇒ Median = 51.5 + 3.4

⇒ Median = 54.9

∴ Median of the data set = 54.9

Elementary Statistics Question 2:

The median of the observations 49, 91, 24, 46, 90, 20, 21, 14, 66, 32 and 92 is:

  1. 49
  2. 32
  3. 24
  4. 46

Answer (Detailed Solution Below)

Option 4 : 46

Elementary Statistics Question 2 Detailed Solution

Given:

Observations: 49, 91, 24, 46, 90, 20, 21, 14, 66, 32, 92

Formula used:

Median is the middle value of the dataset when the observations are arranged in ascending order.

Calculation:

The observations in ascending order:

14, 20, 21, 24, 32, 46, 49, 66, 90, 91, 92

Total number of observations = 11 (Odd)

Median = Middle observation = Observation at position (n+1)/2

⇒ Median = Observation at position (11+1)/2 = Observation at position 6

⇒ Median = 46

∴ The correct answer is option (4).

Elementary Statistics Question 3:

What is the mean of the following distribution?

Marks  13   27   59   61   97 
No. of Students  95   57   80   98   73

  1. 74
  2. 51
  3. 45
  4. 31

Answer (Detailed Solution Below)

Option 2 : 51

Elementary Statistics Question 3 Detailed Solution

Given:

Marks = {13, 27, 59, 61, 97}

No. of Students = {95, 57, 80, 98, 73}

Formula used:

Mean =

Calculation:

Product of Marks and No. of Students:

13 × 95 = 1235

27 × 57 = 1539

59 × 80 = 4720

61 × 98 = 5978

97 × 73 = 7081

Sum of products:

⇒ 1235 + 1539 + 4720 + 5978 + 7081 = 20553

Total No. of Students:

⇒ 95 + 57 + 80 + 98 + 73 = 403

Mean:

⇒ Mean =

⇒ Mean ≈ 51

∴ The correct answer is option (2).

Elementary Statistics Question 4:

The median of the observations 87, 56, 79, 81, 11, 53, 94, 45, 32, 99 and 98 is:

  1. 53
  2. 56
  3. 81
  4. 79

Answer (Detailed Solution Below)

Option 4 : 79

Elementary Statistics Question 4 Detailed Solution

Given:

The observations are: 87, 56, 79, 81, 11, 53, 94, 45, 32, 99, 98

Formula used:

The median is the middle value of a dataset when arranged in ascending order. If the number of observations is odd, the median is the middle value. If the number is even, the median is the average of the two middle values.

Calculations:

Arrange the observations in ascending order:

11, 32, 45, 53, 56, 79, 81, 87, 94, 98, 99

Count the number of observations:

Total observations = 11 (odd number)

Find the middle value:

Middle observation = (11 + 1) ÷ 2 = 6th observation

6th observation = 79

∴ The median is 79. The correct answer is option (4).

Elementary Statistics Question 5:

The mode and median of a data set is 14.2 and 60, respectively. What is the mean of the data set? (Use empirical formula.)

  1. 86.9
  2. 80.4
  3. 82.9
  4. 88.6

Answer (Detailed Solution Below)

Option 3 : 82.9

Elementary Statistics Question 5 Detailed Solution

Given:

Mode = 14.2

Median = 60

Empirical formula: Mean = (3 × Median - 2 × Mode) / 1

Formula Used:

Mean = (3 × Median - 2 × Mode)

Calculation:

Substitute values:

⇒ Mean = (3 × 60 - 2 × 14.2)

⇒ Mean = (180 - 28.4)

⇒ Mean = 151.6 / 1

⇒ Mean = 82.9

The mean of the data set is 82.9.

Top Elementary Statistics MCQ Objective Questions

If Mode is 8 and mean – median = 12 then find the value of mean?

  1. 48
  2. 56
  3. 72
  4. 44

Answer (Detailed Solution Below)

Option 4 : 44

Elementary Statistics Question 6 Detailed Solution

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Given:

If mode = 8 and mean – median = 12

Formula used

Mode = mean – 3 (mean - median)

Mode = 3median - 2mean

Calculation

We know that, Mode = mean – 3(mean -median)

Put the value, 8 = mean – 3 (12)

Mean = 36 + 8 = 44

What is the Mode of the following data:

X

32

14

59

41

28

7

34

20

f(x)

8

4

12

8

10

16

15

9

  1. 28
  2. 14
  3. 7
  4. 59

Answer (Detailed Solution Below)

Option 3 : 7

Elementary Statistics Question 7 Detailed Solution

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Concept:

The mode is the value that appears most often in a set of data values.

Calculation:

32 occurred 8 times

14 occurred 4 times

59 occurred 12 times

41 occurred 8 times 

28 occurred 10 times

7 occurred 16 times 

34 occurred 15 times

20 occurred 9 times

∴ Mode will be 7

If the difference between the mode and median is 2, then find the difference between the median and mean(in the given order).

  1. 2
  2. 1
  3. 3
  4. 4

Answer (Detailed Solution Below)

Option 2 : 1

Elementary Statistics Question 8 Detailed Solution

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Concept:

Relation between mode, median and mean is given by:

Mode = 3 × median – 2 × mean

Calculation:

Given:

Mode – median = 2

As we know

Mode = 3 × median – 2 × mean

Now, Mode = median + 2

⇒ (2 + median) = 3median – 2mean   

⇒ 2Median - 2Mean = 2

⇒ Median - Mean = 1

∴ The difference between the median and mean is 1.

Find the variance of the given numbers: 36, 28, 45, and 51.

  1. 63.5
  2. 68.5
  3. 71.5
  4. 76.5

Answer (Detailed Solution Below)

Option 4 : 76.5

Elementary Statistics Question 9 Detailed Solution

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Mean is the average of the given numbers,

⇒ Mean = (36 + 28 + 45 + 51)/4 = 160/4 = 40

Variance is calculated by taking the average of the squares of the difference between each term and the mean,

⇒ Variance = [(36 - 40)2 + (28 - 40)2 + (45 - 40)2 + (51 - 40)2]/4

= [16 + 144 + 25 + 121]/4 = 306/4 = 76.5

∴ Variance of the given numbers = 76.5

The mean deviation of the data 3, 10, 10, 4, 7, 10, 5 from mean is :

  1. 7
  2. 19/7
  3. 50/7
  4. 18/7

Answer (Detailed Solution Below)

Option 4 : 18/7

Elementary Statistics Question 10 Detailed Solution

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Given:

Data is 3, 10, 10, 4, 7, 10, 5 

Formula used:

Average deviation about the mean 

 where x̅ = Mean

xi = individual term 

n = total number of terms

Mean = Sum of all the terms/Total number of terms

Calculation:

n = total numbers in a data = 7

Mean x̅ = (3 + 10 + 10 + 4 + 7 + 10 + 5)/7 = 7

Mean deviation from mean =

Mean deviation from mean = (1/7) × [4 + 3 + 3 + 3 + 0 + 3 + 2]

∴ Mean deviation = 18/7

Mean of five consecutive even numbers is 16, find the variance of the numbers.

  1. 40
  2. 16
  3. 8
  4. 10

Answer (Detailed Solution Below)

Option 3 : 8

Elementary Statistics Question 11 Detailed Solution

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Given:

Mean of five consecutive even numbers = 16

Formula used:

V = variance

∑ = summation

x = observation

n = number of observations

a = 1st term of the numbers

d = common difference

Calculation:

⇒ 2a + (5 – 1)2 = 32

⇒ 2a + 4 × 2 = 32

⇒ 2a = 32 – 8

⇒ 2a = 24

⇒ a = 12

1st term = 12

Other terms are 14, 16, 18, 20

⇒ 

⇒ 

⇒ 8

⇒ V = 8

∴ The variance of the numbers is 8

Find the mean deviation of 3, 4, 5, 7, 10, 10, 10

  1. 18/7
  2. 17/7
  3. 14/7
  4. 11/7

Answer (Detailed Solution Below)

Option 1 : 18/7

Elementary Statistics Question 12 Detailed Solution

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Given

3, 4, 5, 7, 10, 10, 10

Concept used

Mean = Average

Deviation is the difference with the given number in the series.

Calculation

Mean = 

Mean = 49/7

Mean = 7

Checking the mean deviation with all the numbers given in the series.

Mean deviation 

⇒ |7 - 3|, |7 - 4|, |7 - 5|, |7 - 7|, |7 - 10|, |7 - 10|, |7 - 10|

⇒ 4, 3, 2, 0, 3, 3, 3

Mean deviation = 

Mean deviation = 18/7

In a frequency distribution, the mid value of a class is 12 and its width is 6. The lower limit of the class is:

  1. `1
  2. 18
  3. 6
  4. 9

Answer (Detailed Solution Below)

Option 4 : 9

Elementary Statistics Question 13 Detailed Solution

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Given:

The mid value of a class = 12

Width = 6

Formula used:

Lower limit = Mid value – width/2

Calculation:

Lower limit = 12 – 6/2

⇒ 12 – 3

⇒ 9

∴ The lower limit of the class is 9

The standard deviation of a data set is given as 34. What will be the variance of the data set?

  1. 1122
  2. 1156
  3. 578
  4. 1196

Answer (Detailed Solution Below)

Option 2 : 1156

Elementary Statistics Question 14 Detailed Solution

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GIVEN :

The standard deviation of a data set is given as 34.

CONCEPT :

The value of variance is the square of standard deviation.

FORMULA USED :
Standard Deviation = √Variance

CALCULATION :  

Using the formula :

Variance of the set of data = 342 = 1156

Find the standard deviation of {7, 13, 15, 11, 4}

  1. 16
  2. 25
  3. 5
  4. 4

Answer (Detailed Solution Below)

Option 4 : 4

Elementary Statistics Question 15 Detailed Solution

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Given:

7, 13, 15, 11, 4

Formula used:

 

Mean (m) = Total of observations/number of observations

S.D = standard deviation

∑ = summation

x = observation

m = mean of the observations

n = number of observation

Calculation:

Mean of 7, 13, 15, 11, 4

⇒ 50/5

⇒ 10

⇒ 

⇒ 

⇒ √16

⇒ 4

∴ The standard deviation is 4 

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