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

To find the mean, we construct the table under. Taking assumed mean a = 63 Numbers ( x i ) d i = x i - a ( a = 63 ) Cumulative frequency Frequency ( f i ) d i f i 60 - 3 8 8 - 24 61 - 2 18 10 - 20 62 - 1 33 15 - 15 63 0 40 7 0 64 1 49 9 9 65 2 55 6 12 66 3 60 5 15 Total 60 - 23 Mean = a + ∑ d i f i ∑ f i = 63 + ( - 23 ) 60 = 3757 60 ≈ 62 . 617 Hence, the obtained mean is 62 . 62 .

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 .

MEDIUM

10th ICSE

IMPORTANT

Earn 100

Find the mean of the following distribution:

Number $5$ $10$ $15$ $20$ $25$ $30$ $35$

Frequency $1$ $2$ $5$ $6$ $3$ $2$ $1$

50% studentsanswered this correctly

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 7

The contents of $100$ matchboxes were checked to determine the number of matches they contained:

No. of matches	$35$	$36$	$37$	$38$	$39$	$40$	$41$
No. of boxes	$6$	$10$	$18$	$25$	$21$	$12$	$8$

Calculate, correct to one decimal place, the mean number of matches per box.

MEDIUM

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 21 - Measures of Central Tendency>Exercise 21.1>Q 7

The contents of $100$ matchboxes were checked to determine the number of matches they contained:

No. of matches	$35$	$36$	$37$	$38$	$39$	$40$	$41$
No. of boxes	$6$	$10$	$18$	$25$	$21$	$12$	$8$

Determine how many extra matches would have to be added to the total contents of the $100$ boxes to bring the mean up to exactly 39 matches.

MEDIUM

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 21 - Measures of Central Tendency>Exercise 21.1>Q 8

Find the mean for the following distribution:

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

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	$8$	$5$	$12$	$35$	$24$	$16$

Number	$5$	$10$	$15$	$20$	$25$	$30$	$35$
Frequency	$1$	$2$	$5$	$6$	$3$	$2$	$1$

Find the mean of the following distribution: Number 5 10 15 20 25 30 35 Frequency 1 2 5 6 3 2 1

Important Questions on Measures of Central Tendency

Learn and Prepare for any exam you want !

Find the mean of the following distribution:

Number $5$ $10$ $15$ $20$ $25$ $30$ $35$

Frequency $1$ $2$ $5$ $6$ $3$ $2$ $1$