The weights of coffee in 70 jars are shown in the following table: Weight (in grams ) 200 - 201 201 - 202 202 - 203 203 - 204 204 - 205 205 - 206 Frequency 13 27 18 10 1 1 Determine variance and standard deviation of the above distribution.

Weight (in grams ) Class mark x i f i d i = x i - A A = 202 . 5 f i u i f i d i 2 200 - 201 200 . 5 13 - 2 - 26 52 201 - 202 201 . 5 27 - 1 - 27 27 202 - 203 202 . 5 18 0 0 0 203 - 204 203 . 5 10 1 10 10 204 - 205 204 . 5 1 2 2 4 205 - 206 205 . 5 1 3 3 9 ∑ f i = 70 ∑ f i u i = - 38 ∑ f i d i 2 = 102 Thus, by step deviation method, σ = S.D = Σ f i d i 2 Σ f i − Σ f i d i Σ f i 2 = 102 70 − − 38 70 2 = 1 .457 − 0 .2946 = 1 .1623 ≈ 1 .08 And variance = σ 2 = 1 . 16 .

HARD

11th ICSE

IMPORTANT

Earn 100

Find the mean, variance and standard deviation for the following data by using step deviation method:

Classes $10 - 20$ $20 - 30$ $30 - 40$ $40 - 50$ $50 - 60$ $60 - 70$ $70 - 80$ $80 - 90$ $90 - 100$

Frequency $3$ $4$ $7$ $7$ $15$ $9$ $6$ $6$ $3$

Important Questions on Statistics

HARD

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 14 - Statistics>EXERCISE>Q 13

The weights of coffee in $70 - 80$ jars are shown in the following table:

Weight (in $grams$ )	$20$	$201 - 202$	$202 - 203$	$203 - 204$	$204 - 205$	$205 - 206$
Frequency	$13$	$90 - 100$	$18$	$10$	$1$	$1$

Determine variance and standard deviation of the above distribution.

HARD

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 14 - Statistics>EXERCISE>Q 14

The heights to the nearest

cm

, of

30

men are

159, 170, 174, 173, 175, 160, 161, 164, 163, 165,

164, 171, 162, 170, 177, 185, 181, 180, 175, 165, 186, 174, 168, 168, 176, 176, 165, 175, 167

and

180 .

Using class intervals

= [\frac{\sum f_{i} u_{i}^{2}}{Σ f_{i}} - {(\frac{Σ f_{i} u_{i}}{Σ f_{i}})}^{2}] \times C^{2}

draw up a grouped frequency distribution and use this to estimate the arithmetic mean and the standard deviation.

MEDIUM

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 14 - Statistics>EXERCISE>Q 15

The mean of

5

observations is

6

and the standard deviation is

2 .

If the three observations are

= [\frac{254}{60} - {(\frac{6}{60})}^{2}] \times 100

and

9

, find the other two observations.

MEDIUM

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 14 - Statistics>EXERCISE>Q 16

The mean and the variance of

5

observations are

4.4

and

8.24

respectively. If the three observations are

1, 2

and

6,

find the other two observations.

EASY

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 14 - Statistics>EXERCISE>Q 17

The variance of

20

observations is

5 .

If each observation is multiplied by

2,

find the new variance of the resulting observations.

MEDIUM

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 14 - Statistics>EXERCISE>Q 18

While calculating the mean and variance of

10

readings, a student wrongly uses the reading

52

for the correct reading

25 .

He obtained the mean and variance as

45

and

16

respectively. Find the correct mean and variance.

EASY

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 14 - Statistics>EXERCISE>Q 1

If the coefficient of variation of a distribution is

75

and standard deviation is

27,

then what is the arithmetic mean?

EASY

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 14 - Statistics>EXERCISE>Q 2

If the variance of monthly wages paid to workers by two firms A and B are

100

and

81

respectively and if the firms have same average monthly wages, then which firms shows greater variability in individual wages?

Classes	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$	$80 - 90$	$90 - 100$
Frequency	$3$	$4$	$7$	$7$	$15$	$9$	$6$	$6$	$3$

Find the mean, variance and standard deviation for the following data by using step deviation method: Classes 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100 Frequency 3 4 7 7 15 9 6 6 3

Important Questions on Statistics

Learn and Prepare for any exam you want !

Find the mean, variance and standard deviation for the following data by using step deviation method:

Classes $10 - 20$ $20 - 30$ $30 - 40$ $40 - 50$ $50 - 60$ $60 - 70$ $70 - 80$ $80 - 90$ $90 - 100$

Frequency $3$ $4$ $7$ $7$ $15$ $9$ $6$ $6$ $3$