The following table gives the wages of workers in a factory: Wages in Z 45 - 50 50 - 55 55 - 60 60 - 65 65 - 70 70 - 75 75 - 80 No. of workers 5 8 30 25 14 12 6 Calculate the mean by the shortcut method.

Here, the class size ( h ) = 5 let a assumed mean be A = 62 . 5 . Then the frequency distribution table as given below: Wages in Z frequency f i Mid value x i Step deviation u i = x i - A h f i u i 45-50 5 47.5 -3 -15 50-55 8 52.5 -2 -16 55-60 30 57.5 -1 -30 60-65 25 62.5 0 0 65-70 14 67.5 1 14 70-75 12 72.5 2 24 75-80 6 77.5 3 18 Σf i = 100 Σf i u i = - 5 So, mean = A + Σf i u i Σf i × h = 62 . 5 + - 5 100 × 5 Or mean = 62 . 5 - 0 . 25 = 62 . 25

Calculate the mean of the distribution given below using the short cut method. Marks 11 - 20 21 - 30 31 - 40 41 - 50 51 - 60 61 - 70 71 - 80 No. of students 2 6 10 12 9 7 4

We shall use short-cut method by taking assumed mean (A) = 45 . 5 Marks Mid Values x i Frequency f i d i = x i - A f i d i 11 - 20 15 . 5 2 - 30 - 60 21 - 30 25 . 5 6 - 20 - 120 31 - 40 35 . 5 10 - 10 - 100 41 - 50 45 . 5 12 0 0 51 - 60 55 . 5 9 10 90 61 - 70 65 . 5 7 20 140 71 - 80 75 . 5 4 30 120 Total 50 70 Mean x - = a + Σ f i d i Σ f i Mean = 45 . 5 + 70 50 Mean = 45 . 5 + 1 . 4 Mean = 46 . 9 Hence, the mean is 46 . 9 .

If the mean of the given distribution is 24 , find the value of ' a ' . Marks 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 Number of Students 7 a 8 10 5

Given, Marks 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 Number of Students 7 a 8 10 5 Marks Number of students Class Mark (x) f(x) 0 - 10 7 5 35 10 - 20 a 15 15 a 20 - 30 8 25 200 30 - 40 10 35 350 40 - 50 5 45 225 ∑ f = 30 + a ∑ f ( x ) = 810 + 15 a ∑ f ( x ) ∑ f = 24 ⇒ 810 + 15 a 30 + a = 24 ⇒ 810 + 15 a = 720 + 24 a ⇒ 90 = 9 a ⇒ a = 10 Hence, a = 10 .

The following table gives the life time in days of 100 electricity tubes of a certain make: Lifetime in days No. of tubes less than 50 8 less than 100 23 less than 150 55 less than 200 81 less than 2 . 50 93 less than 300 100 Find the mean lifetime of electricity tubes.

We will use Step Deviation Method First of all, we have to find class mark for each interval. We know that, Class mark x i = upper class limi t + lowe r class limit 2 Let us take 175 as assumed mean ( a ). Class size (h) = 50 Class interval Number of tubes (cf) Class mark ( x i ) d i = x i - 17 u i = d i h Frequency ( f i ) f i u i 0 - 50 8 25 - 150 - 3 8 - 24 50 - 100 23 75 - 100 - 2 15 - 30 100 - 150 55 125 - 50 - 1 32 - 32 150 - 200 81 175 0 0 26 0 200 - 250 93 225 50 1 12 12 250 - 300 100 275 100 2 7 14 Total Σ f i = 100 Σ f i u i = 60 Now, we can see that X = A + h × Σf i u i Σf i = 175 + 50 × - 60 100 = 175 + 50 × - 0 . 60 = 145 Hence, the mean of the electricity tubes is 145 .

HARD

10th ICSE

IMPORTANT

Earn 100

The data on the number of patients attending a hospital in a month is given below. Find the average (mean) number of patients attending the hospital in a month using the short cut method.

Take assumed mean as $45$ . Give your answer correct to $2$ decimal places.

Number of patients $10 - 20$ $20 - 30$ $30 - 40$ $40 - 50$ $50 - 60$ $60 - 70$

Number of days $5$ $2$ $7$ $9$ $2$ $5$

Important Questions on Measures of Central Tendency

HARD

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 21 - Measures of Central Tendency>Exercise 21.1>Q 15

The following table gives the wages of workers in a factory:

Wages in Z	$45 - 50$	$50 - 55$	$= 45 + \frac{(- 140)}{30}$	$60 - 65$	$65 - 70$	$70 - 75$	$75 - 80$
No. of workers	$5$	$8$	$= 40.33$	$25$	$14$	$12$	$6$

Calculate the mean by the shortcut method.

HARD

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 21 - Measures of Central Tendency>Exercise 21.1>Q 16

Calculate the mean of the distribution given below using the short cut method.

Marks	$11 - 20$	$21 - 30$	$31 - 40$	$41 - 50$	$51 - 60$	$61 - 70$	$71 - 80$
No. of students	$2$	$6$	$10$	$12$	$9$	$7$	$4$

HARD

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 21 - Measures of Central Tendency>Exercise 21.1>Q 17

A class teacher has the following absentee record of $40$ students of a class for the whole term. Find the mean number of days a student was absent.

Number of days	$0 - 6$	$6 - 10$	$10 - 14$	$14 - 20$	$20 - 28$	$28 - 38$	$38 - 40$
Number of students	$11$	$10$	$7$	$4$	$4$	$3$	$1$

HARD

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 21 - Measures of Central Tendency>Exercise 21.1>Q 18

If the mean of the given distribution is $24$ , find the value of $' a'$ .

Marks	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$
Number of Students	$7$	$a$	$8$	$10$	$5$

HARD

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 21 - Measures of Central Tendency>Exercise 21.1>Q 19

The mean of the following frequency distribution is $57.6$ and the sum of all the frequencies is $50$ . Find the values of $p$ and $q$ :

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

HARD

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 21 - Measures of Central Tendency>Exercise 21.1>Q 20

The following table gives the life time in days of $100$ electricity tubes of a certain make:

Lifetime in days	No. of tubes
less than $50$	$8$
less than $100$	$23$
less than $150$	$55$
less than $200$	$81$
less than $2.50$	$93$
less than $300$	$100$

Find the mean lifetime of electricity tubes.

HARD

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 21 - Measures of Central Tendency>Exercise 21.1>Q 21

Using the information given in the adjoining histogram, calculate the mean correct to one decimal place.

Question Image

HARD

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 21 - Measures of Central Tendency>Exercise 21.2>Q 1

A student scored the following marks in

11

questions of a question paper:

7, 3, 4, 1, 5, 8, 2, 2, 5, 7, 6

. Find the median marks.

Number of patients	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$
Number of days	$5$	$2$	$7$	$9$	$2$	$5$

Important Questions on Measures of Central Tendency

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