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

Given:

Marks = [19, 36, 60, 69, 85]

No. of Students = [63, 62, 59, 17, 70]

Formula Used:

Mean = (Σ(f_i × x_i)) / Σ(f_i)

Where:

f_i = Frequency (No. of Students)

x_i = Marks

Calculation:

f_i × x_i:

19 × 63 = 1197

36 × 62 = 2232

60 × 59 = 3540

69 × 17 = 1173

85 × 70 = 5950

Σ(f_i × x_i) = 1197 + 2232 + 3540 + 1173 + 5950 = 14092

Σ(f_i) = 63 + 62 + 59 + 17 + 70 = 271

Mean:

⇒ Mean = Σ(f_i × x_i) / Σ(f_i)

⇒ Mean = 14092 / 271

⇒ Mean = 52

The mean of the distribution is 52.

Given:

Marks obtained by students: 45, 67, 80, 56, 72

Formula Used:

Range = Highest value - Lowest value

Calculation:

Highest value = 80

Lowest value = 45

⇒ Range = 80 - 45

⇒ Range = 35

The range of the marks is 35.

Given:

Marks of 12 students: x, 28, 35, 56, 78, 63, 65, 81, 79, 83, 80, y

Range = 70

Average = 64

x = Lowest mark, y = Highest mark

Formula used:

Range = y - x

Average =

Calculation:

Range = y - x

⇒ 70 = y - x

⇒ y = x + 70

Average =

⇒ 64 =

⇒ 64 × 12 = x + 28 + 35 + 56 + 78 + 63 + 65 + 81 + 79 + 83 + 80 + y

⇒ 768 = x + y + (28 + 35 + 56 + 78 + 63 + 65 + 81 + 79 + 83 + 80)

⇒ 768 = x + y + 648

⇒ x + y = 768 - 648

⇒ x + y = 120

Solving for x and y:

From y = x + 70 and x + y = 120, substitute y = x + 70:

⇒ x + (x + 70) = 120

⇒ 2x + 70 = 120

⇒ 2x = 120 - 70

⇒ 2x = 50

⇒ x = 25

Substitute x = 25 in y = x + 70:

⇒ y = 25 + 70

⇒ y = 95

∴ The ordered pair (x, y) = (25, 95).

The correct answer is option (3).

Given:

Classes: 125–130(30), 130–135(30), 135–140(33), 140–145(x), 145–150(31)

Formula used:

Where: Modal class = one containing the mode (140–145):

l = 140, f₁ = x, f₀ = 33, f₂ = 31, h = 5

Calculations:

Mode = 140, so

⇒

⇒ 5x - 165 = 0

⇒ x = 165/5

⇒ x = 33

∴ The correct answer is option 1.

Given:

Mode = 28.4

Median = 88

Formula used:

Or,

Calculation:

Using formula:

⇒ Mean - 28.4 = 3Mean - 264

⇒ -28.4 + 264 = 3Mean - Mean

⇒ 235.6 = 2Mean

⇒ Mean = 117.8

∴ The correct answer is .

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