Find the mean and the standard deviation for the following data: Number of children 0 - 2 2 - 4 4 - 6 6 - 8 8 - 10 10 - 12 Number of families 272 328 205 120 15 10

Number of children x i Class mark f i d i = x i - A A = 5 u i = d i C C = 2 f i u i f i u i 2 0 - 2 1 272 - 4 - 2 - 544 1088 2 - 4 3 328 - 2 - 1 - 328 328 4 - 6 5 205 0 0 0 0 6 - 8 7 120 2 1 120 120 8 - 10 9 15 4 2 30 60 10 - 12 11 10 6 3 30 90 Σ f i = 950 Σ f i u i = - 692 Σ f i u i 2 = 1686 By step deviation method mean x ¯ = A + ∑ f i u l Σ f i × C = 5 − 692 950 × 2 = 3 .54 And, S . D = σ = ∑ f i u i 2 Σ f i − Σ f i u i Σ f i 2 × C = 1686 950 − − 692 950 2 × 2 = 1 .77474 − 0 .5306 × 2 = 2 .23

Find the mean and variance of the following data by using step deviation method: Classes 0 - 5 5 - 10 10 - 15 15 - 20 20 - 25 25 - 30 30 - 35 35 - 40 40 - 45 Frequency 20 24 32 28 20 11 26 15 24

Classes Class Mark x i f i d i = x i - A A = 22 . 5 u i = d i C C = 5 f i u i f i u i 2 0 - 5 2 . 5 20 - 20 - 4 - 80 320 5 - 10 7 . 5 24 - 15 - 3 - 72 216 10 - 15 12 . 5 32 - 10 - 2 - 64 128 15 - 20 17 . 5 28 - 5 - 1 - 28 28 20 - 25 22 . 5 20 - 0 0 0 0 25 - 30 27 . 5 11 5 1 11 11 30 - 35 32 . 5 26 10 2 52 104 35 - 40 37 . 5 15 15 3 45 135 40 - 45 42 . 5 24 20 4 96 384 Σ f i = 200 Σ f i u i = - 40 Σ f i u i 2 = 1326 By step deviation method, mean = A + Σ f i u i Σ f i × C = 22 .5 − 40 200 × 5 = 22 .5 − 1 = 21 .5 And, S.D ( σ ) = ∑ f i u i 2 Σ f i − Σ f i u i Σ f i 2 × C = 1326 200 − − 40 200 2 × 5 = 6 .63 − 0 .04 × 5 = 12 .83549 So, variance, σ 2 = 164 .75

HARD

11th ICSE

IMPORTANT

Earn 100

Find the mean deviation from the mean as well as from the median for the following series:

$x$ $10$ $11$ $12$ $13$ $14$

Frequency $3$ $12$ $18$ $12$ $3$

Important Questions on Statistics

HARD

11th ICSE

IMPORTANT

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

Find the mean deviation from the mean as well as from the median for the following series:

Class	$2 - 4$	$4 - 6$	$6 - 8$	$8 - 10$
Frequency	$3$	$\begin{matrix} Σ f \|x - M_{d}\| \\ = 36 \end{matrix}$	$2$	$1$

MEDIUM

11th ICSE

IMPORTANT

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

Find the mean deviation about the median of the following frequency distribution:

Class	$0 - 6$	$6 - 12$	$12 - 18$	$18 - 24$	$24 - 30$
Frequency	$8$	$10$	$12$	$9$	$5$

(Write the answer upto two decimal places.)

HARD

11th ICSE

IMPORTANT

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

Find the mean deviation from the mean of the following data:

Marks	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$
Number of students	$= \frac{\sum f \|x - M_{d}\|}{\sum f}$	$8$	$15$	$16$	$6$

MEDIUM

11th ICSE

IMPORTANT

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

The annual rainfall in $centimetres$ at a place $A$ over the period $2009$ to $2014$ was as follows:

Year	$2009$	$2010$	$2011$	$2012$	$2013$	$2014$
Rainfall $(cm)$	$73$	$79$	$111$	$79$	$55$	$59$

Examine the mean rainfall and the standard deviation.

MEDIUM

11th ICSE

IMPORTANT

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

The following data relates to the goods produced in a factory. Find the mean and the standard deviation of the daily output of the articles produced.

Number of articles	$18$	$19$	$20$	$21$	$22$	$23$	$24$	$25$	$26$	$27$
Number of workers	$3$	$7$	$11$	$14$	$18$	$17$	$13$	$8$	$5$	$4$

MEDIUM

11th ICSE

IMPORTANT

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

Determine the mean and standard deviation for the following distribution: (Write the answer upto two decimal places.)

Marks	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$	$12$	$13$	$14$	$15$	$16$
Frequency	$1$	$6$	$6$	$8$	$8$	$2$	$2$	$3$	$0$	$2$	$1$	$0$	$0$	$0$	$1$

HARD

11th ICSE

IMPORTANT

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

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

Number of children	$0 - 2$	$2 - 4$	$4 - 6$	$6 - 8$	$8 - 10$	$10 - 12$
Number of families	$272$	$328$	$205$	$120$	$15$	$10$

HARD

11th ICSE

IMPORTANT

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

Find the mean and variance of the following data by using step deviation method:

Classes	$0 - 5$	$5 - 10$	$10 - 15$	$15 - 20$	$20 - 25$	$25 - 30$	$30 - 35$	$35 - 40$	$40 - 45$
Frequency	$20$	$24$	$32$	$28$	$20$	$11$	$26$	$15$	$24$

Find the mean deviation from the mean as well as from the median for the following series: x 10 11 12 13 14 Frequency 3 12 18 12 3

Important Questions on Statistics

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Find the mean deviation from the mean as well as from the median for the following series:

$x$ $10$ $11$ $12$ $13$ $14$

Frequency $3$ $12$ $18$ $12$ $3$