If the mean of the following distribution is 7 . 5 , find the missing frequency f : Variate 5 6 7 8 9 10 11 12 Frequency 20 17 f 10 8 6 7 6

Variate ( x i ) Frequency( f i ) x i f i 5 20 100 6 17 102 7 f 7 f 8 10 80 9 8 72 10 6 60 11 7 77 12 6 72 Total 74 + f 563 + 7 f Mean = ∑ x i f i ∑ f i ⇒ 7 . 5 = 563 + 7 f 74 + f ⇒ 7 . 5 × 74 + f = 563 + 7 f ⇒ 555 + 7 . 5 f = 563 + 7 f ⇒ 7 . 5 f - 7 f = 563 - 555 ⇒ 0 . 5 f = 8 ⇒ f = 8 7 . 5 ⇒ f = 16 Hence, the value of f is 16 .

Marks obtained by 40 students in a short assessment is given below, where a and b are two missing data: Marks 5 6 7 8 9 No. of students 6 a 16 13 b If the mean of the distribution is 7 . 2 , find a and b .

Marks ( x i ) No. of students ( f i ) x i f i 5 6 30 6 a 6 a 7 16 112 8 13 104 9 b 9 b Mean = ∑ x i f i ∑ f i ⇒ 7 . 2 = 246 + 6 a + 9 b 40 ⇒ 288 = 246 + 6 a + 9 b ⇒ 2 a + 3 b = 14 ...... ( i ) Also, 35 + a + b = 40 ⇒ a + b = 5 .......... ( i i ) From equations ( i ) and ( i i ) , we get a = 1 , b = 4

Calculate the mean of the following distribution: Class interval 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 Frequency 8 5 12 35 24 16

Class interval Mid-value (Xi) Frequency ( f i ) x i f i 0 - 10 5 8 40 10 - 20 15 5 75 20 - 30 25 12 300 30 - 40 35 35 1225 40 - 50 45 24 1080 50 - 60 55 16 880 Total 100 3600 Mean = ∑ x i f i ∑ f i ⇒ Mean = 3600 100 ⇒ Mean = 36 Hence, the means is 36 .

Calculate the mean of the following distribution using step-deviation method Marks Number of students 0 - 10 10 10 - 20 9 20 - 30 25 30 - 40 30 40 - 50 16 50 - 60 10

Class Interval Mid Values x i Frequency f i d i = x i - A u i = x i - A h f i u i 0 - 10 5 10 - 20 - 2 - 20 10 - 20 15 9 - 10 - 1 - 9 20 - 30 25 25 0 0 0 30 - 40 35 30 10 1 30 40 - 50 45 16 20 2 32 50 - 60 55 10 30 3 30 Let A = 25 and h = 10 X = A + h × Σf i u i Σf i = 25 + 10 × 63 100 = 25 + 6 . 3 = 31 . 3 Hence, the mean is 31 . 3

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

MEDIUM

10th ICSE

IMPORTANT

Earn 100

Find the mean for the following distribution:

Numbers $60$ $61$ $62$ $63$ $64$ $65$ $66$

Cumulative frequency $8$ $18$ $33$ $40$ $49$ $55$ $60$

Important Questions on Measures of Central Tendency

MEDIUM

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 21 - Measures of Central Tendency>Exercise 21.1>Q 9

Category	$A$	$B$	$C$	$D$	$E$	$F$	$G$
Wages in $₹$ per day	$50$	$60$	$70$	$80$	$90$	$100$	$110$
No. of workers	$2$	$4$	$8$	$12$	$10$	$6$	$8$

Calculate the mean wage, correct to the nearest rupee.

MEDIUM

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 21 - Measures of Central Tendency>Exercise 21.1>Q 9

Category	$A$	$B$	$C$	$D$	$E$	$F$	$G$
Wages in $₹$ per day	$50$	$60$	$70$	$80$	$90$	$100$	$110$
No. of workers	$2$	$4$	$8$	$12$	$10$	$6$	$8$

If the number of workers in each category is doubled, what would be the new mean wage? correct to the nearest rupee.

HARD

10th ICSE

IMPORTANT

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

If the mean of the following distribution is $7.5$ , find the missing frequency $f$ :

Variate	$5$	$6$	$7$	$8$	$9$	$10$	$11$	$12$
Frequency	$20$	$17$	$f$	$10$	$8$	$6$	$7$	$6$

HARD

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 21 - Measures of Central Tendency>Exercise 21.1>Q 11

Marks obtained by $40$ students in a short assessment is given below, where $a$ and $b$ are two missing data:

Marks	$5$	$6$	$7$	$8$	$9$
No. of students	$6$	$a$	$16$	$13$	$b$

If the mean of the distribution is $7.2$ , find $a$ and $b$ .

HARD

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 21 - Measures of Central Tendency>Exercise 21.1>Q 12

Calculate the mean of the following distribution:

Class interval	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$
Frequency	$8$	$5$	$12$	$35$	$24$	$16$

HARD

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 21 - Measures of Central Tendency>Exercise 21.1>Q 13

Calculate the mean of the following distribution using step-deviation method

Marks	Number of students
$0 - 10$	$10$
$10 - 20$	$9$
$20 - 30$	$25$
$30 - 40$	$30$
$40 - 50$	$16$
$50 - 60$	$10$

HARD

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 21 - Measures of Central Tendency>Exercise 21.1>Q 14

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	$5$	$2$	$7$	$9$	$2$	$5$

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	$45 - 50$	$50 - 55$	$55 - 60$	$60 - 65$	$65 - 70$	$70 - 75$	$75 - 80$
No. of workers	$5$	$8$	$30$	$25$	$14$	$12$	$6$

Calculate the mean by the shortcut method.

Numbers	$60$	$61$	$62$	$63$	$64$	$65$	$66$
Cumulative frequency	$8$	$18$	$33$	$40$	$49$	$55$	$60$

Find the mean for the following distribution: Numbers 60 61 62 63 64 65 66 Cumulative frequency 8 18 33 40 49 55 60

Important Questions on Measures of Central Tendency

Learn and Prepare for any exam you want !

Find the mean for the following distribution:

Numbers $60$ $61$ $62$ $63$ $64$ $65$ $66$

Cumulative frequency $8$ $18$ $33$ $40$ $49$ $55$ $60$