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

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

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).

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).

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).

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.

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

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

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

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

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

Given:

Mean of five consecutive even numbers = 16

Formula used:

V = variance

∑ = summation

x = observation

n = number of observations

a = 1^st term of the numbers

d = common difference

Calculation:

⇒ 2a + (5 – 1)2 = 32

⇒ 2a + 4 × 2 = 32

⇒ 2a = 32 – 8

⇒ 2a = 24

⇒ a = 12

1^st term = 12

Other terms are 14, 16, 18, 20

⇒ 

⇒ 

⇒ 8

⇒ V = 8

∴ The variance of the numbers is 8

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

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

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

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