The heights of 50 children were measured (correct to the nearest cm ) giving the following results: Height (in cm ) 65 66 67 68 69 70 71 72 73 No. of children 1 4 5 7 11 10 6 4 2 Calculate the mean height for this distribution correct to one place of decimal.

Height x No. of children f f x 65 1 65 66 4 264 67 5 335 68 7 476 69 11 759 70 10 700 71 6 426 72 4 288 73 2 146 Total Σ f = 50 Σ f x = 3459 Mean = Σ f x Σ f = 3459 50 = 69 . 18 = 69 . 2 [corrected to one decimal place] Hence, the mean is 69 . 2 cm .

Find the value of p , if the mean of the following distribution is 18 : x f 13 8 15 2 17 3 19 4 20 + p 5 p 23 6

x i f i f i x i 13 8 104 15 2 30 17 3 51 19 4 76 20 + p 5 p 100 p + 5 p 2 23 6 138 Total ∑ f i = 23 + 5 p ∑ f i x i = 399 + 100 p + 5 p 2 Mean = ∑ f i x i ∑ f i ⇒ 18 = 399 + 100 p + 5 p 2 23 + 5 p ⇒ 18 × 23 + 90 p = 399 + 100 p + 5 p 2 ⇒ 5 p 2 + 100 p - 90 p + 399 - 414 = 0 ⇒ 5 p 2 + 10 p - 15 = 0 ⇒ p 2 + 2 p - 3 = 0 ⇒ p 2 + 3 p - p - 3 = 0 ⇒ p p + 3 - 1 p + 3 = 0 ⇒ p + 3 p - 1 = 0 ⇒ Either p + 3 = 0 or p - 1 = 0 ⇒ p = - 3 or p = 1 Frequency can't be negative, so, p = 1

Find the mean age in years from the frequency distribution given below: Age in years 25 - 29 30 - 34 35 - 39 40 - 44 45 - 49 50 - 54 55 - 59 No. of persons 4 14 22 16 6 5 3

The adjusted frequency distribution is: Age in years Class-mark ( x i ) u i = x i - a h ( a = 42 , h = 5 ) No. of persons ( f i ) u i f i 24 . 5 - 29 . 5 27 - 3 4 - 12 29 . 5 - 34 . 5 32 - 2 14 - 28 34 . 5 - 39 . 5 37 - 1 22 - 22 39 . 5 - 44 . 5 42 0 16 0 44 . 5 - 49 . 5 47 1 6 6 49 . 5 - 54 . 5 52 2 5 10 54 . 5 - 59 . 5 57 3 3 9 Mean age = a + ∑ u i f i ∑ f i × h = 42 + - 37 70 × 5 = 42 - 2 . 64 = 39 . 36 years

The mean of the following frequency distribution is 62 . 8 . Find the value of p : Classes 0 - 20 20 - 40 40 - 60 60 - 80 80 - 100 100 - 120 Frequency 5 8 p 12 7 8

Class Frequency ( f i ) Class mark ( x i ) f j x i 0 - 20 5 10 50 20 - 40 8 30 240 40 - 60 p 50 50 p 60 - 80 12 70 840 80 - 100 7 90 630 100 - 120 8 110 880 Total Σ f i = 40 + p Σ f i x i = 2640 + 50 p Mean = Σ f i x i Σ f i 62 . 8 = ( 2640 + 50 p ) ( 40 + p ) [Given mean = 62 . 8 ] 62 . 8 ( 40 + p ) = 2640 + 50 p 2512 + 62 . 8 p = 2640 + 50 p 62 . 8 p - 50 p = 2640 - 2512 12 . 8 p = 128 p = 128 12 . 8 ∴ p = 10 Hence, the value of p is 10 .

The daily expenditure of 100 families are given below. Calculate f 1 and f 2 , if the mean daily expenditure is ₹ 188 . Expenditure (in ₹ ) 140 - 160 160 - 180 180 - 200 200 - 220 220 - 240 No. of families 5 25 f 1 f 2 5

The daily expenditures of 100 families are given in the form of a table For finding the mean of daily expenditures, let us follow the direct method. So, we have Expenditures (in ₹ ) Frequencies f i Class Mark x i f i x i 140 - 160 5 150 750 160 - 180 25 170 4250 180 - 200 f 1 190 190 f 1 200 - 220 f 2 210 210 f 2 220 - 240 5 230 1150 Total 35 + f 1 + f 2 6150 + 190 f 1 + 210 f 2 It is given that mean of daily expenditures = ₹ 188 ⇒ 6150 + 190 f 1 + 210 f 2 35 + f 1 + f 2 = 188 ⇒ 6150 + 190 f 1 + 210 f 2 = 188 35 + f 1 + f 2 ⇒ 6150 + 190 f 1 + 210 f 2 = 6580 + 188 f 1 + 188 f 2 ⇒ 190 f 1 - 188 f 1 + 210 f 2 - 188 f 2 = 6580 - 6150 ⇒ 2 f 1 + 22 f 2 = 430 ⇒ f 1 + 11 f 2 = 215 . . . . i Also, according to the given question, we have ∑ f i = 100 ⇒ 35 + f 1 + f 2 = 100 ⇒ f 1 + f 2 = 65 . . . . i i Subtracting equation i i from equation i , we have 10 f 2 = 215 - 65 = 150 ⇒ f 2 = 15 Substituting the value of f 2 in equation i i , we have f 1 = 65 - 15 = 50 Hence, f 1 = 50 and f 2 = 15

EASY

10th ICSE

IMPORTANT

Earn 100

An ogive curve is used to determine

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Important Questions on Measures of Central Tendency

HARD

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 21 - Measures of Central Tendency>Chapter Test>Q 1

The mean of

20

numbers is

18 .

3

is added to each of the first ten numbers, find the mean of the new set of

20

numbers.

MEDIUM

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 21 - Measures of Central Tendency>Chapter Test>Q 2

The average height of

30

students is

150 cm

. It was detected later that one value of

165 cm

was wrongly copied as

135 cm

for the computation of mean. Find the correct mean.

EASY

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 21 - Measures of Central Tendency>Chapter Test>Q 3

There are

50

students in a class of which

40

are boys and the rest girls. The average weight of the class is

44 k g

and the average weight of the girls is

40 k g

. Find the average weight of the boys.

HARD

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 21 - Measures of Central Tendency>Chapter Test>Q 4

The heights of $50$ children were measured (correct to the nearest $cm$ ) giving the following results:

Height (in $cm$ )	$65$	$66$	$67$	$68$	$69$	$70$	$71$	$72$	$73$
No. of children	$1$	$4$	$5$	$7$	$11$	$10$	$6$	$4$	$2$

Calculate the mean height for this distribution correct to one place of decimal.

HARD

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 21 - Measures of Central Tendency>Chapter Test>Q 5

Find the value of $p$ , if the mean of the following distribution is $18$ :

$x$	$f$
$13$	$8$
$15$	$2$
$17$	$3$
$19$	$4$
$20 + p$	$5 p$
$23$	$6$

HARD

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 21 - Measures of Central Tendency>Chapter Test>Q 6

Find the mean age in years from the frequency distribution given below:

Age in years	$25 - 29$	$30 - 34$	$35 - 39$	$40 - 44$	$45 - 49$	$50 - 54$	$55 - 59$
No. of persons	$4$	$14$	$22$	$16$	$6$	$5$	$3$

HARD

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 21 - Measures of Central Tendency>Chapter Test>Q 7

The mean of the following frequency distribution is $62.8$ . Find the value of $p$ :

Classes	$0 - 20$	$20 - 40$	$40 - 60$	$60 - 80$	$80 - 100$	$100 - 120$
Frequency	$5$	$8$	$p$	$12$	$7$	$8$

MEDIUM

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 21 - Measures of Central Tendency>Chapter Test>Q 8

The daily expenditure of $100$ families are given below. Calculate $f_{1}$ and $f_{2}$ , if the mean daily expenditure is $₹ 188$ .

$\begin{array}{lccccc} Expenditure (in ₹) & 140 - 160 & 160 - 180 & 180 - 200 & 200 - 220 & 220 - 240 \\ No. of families & 5 & 25 & f_{1} & f_{2} & 5 \end{array}$

An ogive curve is used to determine

Important Questions on Measures of Central Tendency

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