If the mean of the distribution is 33 . 2 and the sum of all frequencies is 100 , then find the missing frequencies f 1 and f 2 . class 6 - 14 14 - 22 22 - 30 30 - 38 38 - 46 46 - 54 54 - 62 62 - 70 frequency 11 21 f 1 15 14 8 f 2 6

Solution: Given: Let assumed mean be A = 34 Class width = h = 8 The table for the given data: class x i f i u i = x i - A h f i u i 6 - 14 10 11 - 3 - 33 14 - 22 18 21 - 2 - 42 22 - 30 26 f 1 - 1 - f 1 30 - 38 34 = A 15 0 0 38 - 46 42 14 1 14 46 - 54 50 8 2 16 54 - 62 58 f 2 3 3 f 2 62 - 70 66 6 4 24 Total ∑ f i = 75 + f 1 + f 2 ∑ f i u i = 3 f 2 - f 1 - 21 Hence , ∑ f i = 75 + f 1 + f 2 = 100 f 1 + f 2 = 25 . . . . . ( i ) Mean = A + ∑ f i u i ∑ f i × h 33 . 2 = 34 + 3 f 2 - f 1 - 21 100 × 8 - 0 . 8 = 3 f 2 - f 1 - 21 100 × 8 3 f 2 - f 1 - 21 = - 10 3 f 2 - f 1 = 11 . . . . . . ( ii ) ( i ) + ( ii ) gives 4 f 2 = 36 f 2 = 9 Substituting, the value of f 2 in ( i ) , gives f 1 = 16 Hence , f 1 = 16 and f 2 = 9

Prepare the frequency distribution table for the given data. Marks below 10 below 20 below 30 below 40 below 50 below 60 Number of students 0 15 20 30 35 40

Given data is, Marks below 10 below 20 below 30 below 40 below 50 below 60 Number of students 0 15 20 30 35 40 By observing the above frequency table, we can say that it is a 'below type'. A frequency distribution is a representation, either in a graphical or a chart or a tabular format, that displays the number of observations within a given interval. The interval size depends on the data being analyzed and the goals of the analyst. The distribution table for the given data: Marks Frequency = Number of students 0 - 10 0 10 - 20 15 - 0 = 15 20 - 30 20 - 15 = 5 30 - 40 30 - 20 = 10 40 - 50 35 - 30 = 5 50 - 60 40 - 35 = 5 Hence, the required frequency distribution table is formed above.

Given, below is a cumulative frequency distribution of 'more than type'. Marks Number of students More than or equal to 60 11 More than or equal to 50 23 More than or equal to 40 43 More than or equal to 30 58 More than or equal to 20 72 More than or equal to 10 82 Change the above data into a continuous grouped frequency distribution.

Solution: Given: A cumulative frequency distribution of 'more than type' We need to represent the above data into a continuous distribution. Thus, the continuous grouped frequency distribution for the given data is : Marks Number of students Greater than 60 11 50 - 60 23 - 11 = 12 40 - 50 43 - 23 = 20 30 - 40 58 - 43 = 15 20 - 30 72 - 58 = 14 10 - 20 82 - 72 = 10 Hence, table of grouped frequency distribution is created above.

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IMPORTANT

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The monthly pocket money of students of a class is given in the following frequency distribution

Pocket money $(in ₹)$ $100 - 125$ $125 - 150$ $150 - 175$ $175 - 200$ $200 - 225$

Number of students $14$ $8$ $12$ $5$ $11$

Find the mean of pocket money using step deviation method.

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Important Questions on Statistics

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10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 20 - Statistics>Topic Exercise>Q 13

Calculate the mean of the scores of $20$ students in a Mathematics test.

Marks	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$
Number of students	$2$	$4$	$7$	$6$	$1$

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10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 20 - Statistics>Topic Exercise>Q 14

If the mean of the distribution is $33.2$ and the sum of all frequencies is $100$ , then find the missing frequencies $f_{1}$ and $f_{2}$ .

class	$6 - 14$	$14 - 22$	$22 - 30$	$30 - 38$	$38 - 46$	$46 - 54$	$54 - 62$	$62 - 70$
frequency	$11$	$21$	$f_{1}$	$15$	$14$	$8$	$f_{2}$	$6$

EASY

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 20 - Statistics>Topic Exercise>Q 1

The median of the observations

11

12

14

(x - 2)

(x + 4)

(x + 9)

32

38

and

47

arranged in ascending order is

24

. Find the value of

x

and hence flnd the mean.

EASY

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 20 - Statistics>Topic Exercise>Q 2

Prepare the frequency distribution table for the given data.

Marks	below $10$	below $20$	below $30$	below $40$	below $50$	below $60$
Number of students	$0$	$15$	$20$	$30$	$35$	$40$

EASY

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 20 - Statistics>Topic Exercise>Q 3

Given, below is a cumulative frequency distribution of 'more than type'.

Marks	Number of students
More than or equal to $60$	$11$
More than or equal to $50$	$23$
More than or equal to $40$	$43$
More than or equal to $30$	$58$
More than or equal to $20$	$72$
More than or equal to $10$	$82$

Change the above data into a continuous grouped frequency distribution.

EASY

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 20 - Statistics>Topic Exercise>Q 4

The number of students absent in a school was recorded everyday $147$ for days and the raw data was presented in the form of the following frequency table.

Number of students	Number of days
$5$	$1$
$6$	$5$
$7$	$11$
$8$	$14$
$9$	$16$
$10$	$13$
$11$	$10$
$12$	$70$
$13$	$4$
$15$	$1$
$18$	$1$
$20$	$1$

Find the median of the above data.

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10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 20 - Statistics>Topic Exercise>Q 5

Find the median of the given frequency distribution.

$x$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$y$	$2$	$3$	$6$	$8$	$16$	$12$	$10$	$13$	$9$	$15$

HARD

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 20 - Statistics>Topic Exercise>Q 6

Calculate the median from the given distribution.

Class	$5 - 10$	$10 - 15$	$15 - 20$	$20 - 25$	$25 - 30$	$30 - 35$	$35 - 40$	$40 - 45$
frequency	$5$	$6$	$15$	$16$	$5$	$4$	$2$	$2$

Pocket money $(in ₹)$	$100 - 125$	$125 - 150$	$150 - 175$	$175 - 200$	$200 - 225$
Number of students	$14$	$8$	$12$	$5$	$11$

The monthly pocket money of students of a class is given in the following frequency distribution Pocket money (in ₹) 100-125 125-150 150-175 175-200 200-225 Number of students 14 8 12 5 11 Find the mean of pocket money using step deviation method.

Important Questions on Statistics

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The monthly pocket money of students of a class is given in the following frequency distribution

Pocket money $(in ₹)$ $100 - 125$ $125 - 150$ $150 - 175$ $175 - 200$ $200 - 225$

Number of students $14$ $8$ $12$ $5$ $11$

Find the mean of pocket money using step deviation method.