Find the mean and the standard deviation for the following data: x i 6 10 14 18 24 28 30 f i 2 4 7 12 8 4 3

The table is as below: x i f i f i x i x i - x ¯ 2 f i x i - x ¯ 2 6 2 12 169 338 10 4 40 81 324 14 7 98 25 175 18 12 216 1 12 24 8 192 25 200 28 4 112 81 324 30 3 90 121 363 n = ∑ f i = 40 ∑ f i x i = 760 ∑ f i x i - x ¯ 2 = 1736 By direct method, mean x ¯ = ∑ f i x i ∑ f i = 760 40 = 19 And, S.D σ = ∑ f i x i - x ¯ 2 ∑ f i = 1736 40 = 217 5 = 6 . 59

Find the mean, variance and standard deviation for the following frequency distribution: Classes 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 Frequency 5 8 15 16 6

The table is as below: Classes Class mark x i f i d i = x i - A A = 25 u i = d i C C = 10 f i u i f i u i 2 0 - 10 5 5 - 20 - 2 - 10 20 10 - 20 15 8 - 10 - 1 - 8 8 20 - 30 25 15 0 0 0 0 30 - 40 35 16 10 1 16 16 40 - 50 45 6 20 2 12 24 ∑ f i = 50 ∑ f i u i = 10 ∑ f i u i 2 = 68 Thus, by step deviation method: Mean = A + ∑ f i u i ∑ f i × C = 25 + 10 50 × 10 = 27 Variance = σ 2 = ∑ f i u i 2 ∑ f i - ∑ f i u i ∑ f i 2 × C 2 = 68 50 - 10 50 2 × 100 = 1 . 36 - 0 . 04 × 100 = 1 . 32 × 100 = 132 So, S.D = σ = Variance = 132 = 11 . 49 .

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

The table is as below: Classes Intervals Class marks x i f i d i = x i - A A = 55 u i = d i C C = 10 f i u i f i u i 2 10 - 20 15 3 - 40 - 4 - 12 48 20 - 30 25 4 - 30 - 3 - 12 36 30 - 40 35 7 - 20 - 2 - 14 28 40 - 50 45 7 - 10 - 1 - 7 7 50 - 60 55 15 0 0 0 0 60 - 70 65 9 10 1 9 9 70 - 80 75 6 20 2 12 24 80 - 90 85 6 30 3 18 54 90 - 100 95 3 40 4 12 48 ∑ f i = 60 ∑ f i u i = 6 ∑ f i u i 2 = 254 By step deviation method, x ¯ = A + Σ f i u i Σ f i × C = 55 + 6 60 × 10 = 56 Variance = σ 2 = ∑ f i u i 2 Σ f i − Σ f i u i Σ f i 2 × C 2 = 254 60 − 6 60 2 × 100 = ( 4 .233 − 0 .01 ) × 100 = 422 .33 And, S.D = variance = 422 .33 = 20 .55 .

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 .

MEDIUM

11th ICSE

IMPORTANT

Earn 100

Find the mean, variance and standard deviation of the following marks scored by $10$ students:

$45, 70, 62, 60, 50, 48, 67, 34, 65, 58 .$

Important Questions on Statistics

MEDIUM

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 14 - Statistics>EXERCISE>Q 6

Find the mean and the standard deviation for the following data:

$x_{i}$	$6$	$10$	$14$	$18$	$24$	$28$	$30$
$f_{i}$	$2$	$4$	$7$	$12$	$8$	$4$	$3$

HARD

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 14 - Statistics>EXERCISE>Q 7

Find the standard deviation for the following frequency distribution:

$x$	$2$	$3$	$4$	$5$	$6$	$7$
$f$	$4$	$9$	$16$	$14$	$11$	$6$

(Write the answer upto two decimal places.)

HARD

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 14 - Statistics>EXERCISE>Q 8

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

$x_{i}$	$60$	$61$	$62$	$63$	$64$	$65$	$66$	$67$	$68$
$f_{i}$	$2$	$1$	$12$	$29$	$25$	$12$	$10$	$4$	$5$

HARD

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 14 - Statistics>EXERCISE>Q 9

Find the mean, variance and standard deviation for the following frequency distribution:

Classes	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$
Frequency	$5$	$8$	$15$	$16$	$6$

HARD

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 14 - Statistics>EXERCISE>Q 10

Find the standard deviation from the following table giving the age distribution of $540$ members of parliament.

Age (in years)	$25 - 35$	$35 - 45$	$45 - 55$	$55 - 65$	$65 - 75$
Number	$64$	$132$	$153$	$140$	$51$

(Write the answer upto two decimal places.)

HARD

11th ICSE

IMPORTANT

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

Calculate the mean, variance and standard deviation for the following frequency distribution by using step deviation method:

Classes	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$	$80 - 90$	$90 - 100$
Frequency	$3$	$7$	$12$	$15$	$8$	$3$	$2$

HARD

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 14 - Statistics>EXERCISE>Q 12

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

HARD

11th ICSE

IMPORTANT

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

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.

Find the mean, variance and standard deviation of the following marks scored by 10 students: 45,70,62,60,50,48,67,34,65,58.

Important Questions on Statistics

Learn and Prepare for any exam you want !

Find the mean, variance and standard deviation of the following marks scored by $10$ students:

$45, 70, 62, 60, 50, 48, 67, 34, 65, 58 .$