Elementary Statistics Questions and Answers

Standard deviation =    \sqrt {Variance}

=\sqrt {10.6} = 3.25

Answer : [C]
Explanation :
Mode = 3 Median - 2 Mean
Median = mode + 2 mean / 3
= 26.1 + 2(20.6) /3
= 26.1 + 41.2 / 3
= 67.3/ 3
= 22.43

Arranging the given data in ascending order,
27, 29, 30, 31, 35, 37, 41, 43

Here the number of terms = 9 which is old

Median = n + 1 th term/ 2 = 10/ 2
= 5th term
Median = 35

Explanation :
Average production of Kharif =
32 + 48 + 50 + 36 + 34/5
= 200 / 5
= 40
Average production of Rabi =
25 + 40 + 35 + 75 + 25/ 5
= 200/ 5
= 40
If we compare the least and highest value the variation is less in Kharif and more in Rabi
A is more consistent than B. But the average of both are equal.

S.D. of 11 values = 7
Increment in each value = 9
S.D. is unchanged by the increment in the values.

σ = 7
Variance = σ^{2} = 7^{2} = 49

C.V. for Sehwag =
15/ 58 x 100 = 25.86%
C.V. for Tendulkar =
12/ 48 x 100 = 25%
C.V. for Gambhir =
2/ 14 x 100 = 14.29%
C.V for Gambhir is the least. Hence the batsman Gambhir is more consistent.

Mean height, x̄ = (142 + 150 + 149 + 156 + 153)/5
= 750/5
= 150
Mean, x̄ =150 cm
Thus, the mean height is 150 cm.

2 Mean + Mode = 3 Median

∴2Mean = 3 × 61.6 - 65

∴2Mean = 119.8

⇒ Mean = 119.8/2

⇒ Mean = 59.9

Solution:

Given, n = 5, x̄ = 18

x̄ = ∑xin

∑xi

= 5 × 18 = 90

Thus, the total of 5 numbers = 90

Let the excluded number be "a".

Therefore, total of 4 numbers = 90 - a

Mean of 4 numbers = (90 - a)/4
16 = (90 - a)/4
90 - a = 64
a = 26

⇒ The missing number is 26.

Mean = 17.8
Mode = 12

Answer -mean = 9
6+ 8 + x + 2 + 10 + 2x - 1+ 2 = 54
3x + 27 =54
3x = 54 -27
3x = 27
X =9

Mean = sum of observations/ number of observations
Mean = 7 +16+ 121+ 51+ 101+ 81+1+ 16+ 9+ 11+ 16/11
Mean = 430/11 = 39.09
Median - for median we’ll arrange it in ascending order - 1, 7, 9, 11, 16,16, 16, 51, 81, 101,121
So the median will be \frac{n+1}{2}th term = 6th term = 16
Mode will be 16 as it is maximum

Solution - 33, 36, 38, 39, 43, 44, 44, 44, 46, 51

Therefore, 44 appears maximum times hence it is the mode of the data.

Finding the Mode
l=f1−f02f1−f2−f0×h
Mode =30+(55−30)2(55)−44−30×10
=30+2536×10
=30+25036
=10+6.944
=36.944
Hence, the modal value for the given Frequency Distribution is 36.944.

Mean = 70+ 80+ 70+ 90+ 80+ 100+ 70/7
= 560/7
=80