Chapter 17 Measures of Central Tendency Ex 17.1

Rajasthan Board RBSE Class 10 Maths Chapter 17 Measures of Central Tendency Ex 17.1

Question 1.
If marks obtained by 10 students in maths are 52, 75, 40, 70, 43, 40, 65, 35, 48 and 52 then find arithmetic mean.
Solution :
Given : Total students in class = 10

Thus, arithmetic mean = 52

Question 2.
The monthly salary (in ₹) of assistant workers in a school are ₹1720, ₹1750, ₹1760 and ₹1710, then find arithmetic mean.
Solution :

Thus, required arithmetic mean = ₹1735

Question 3.
If arithmetic mean of digits 3, 4, 8, 5, x, 3, 2, 1 is 4, then find x.
Solution :
Given : A.M. = 4

⇒ 26 + x = 32
⇒ x = 32 – 26 = 6
Thus, x = 6

Question 4.
Runs scored in 10 innings by a cricketer are 60, 62, 56, 64, 0, 57, 33, 27, 9 and 71. Find average run scored in these innings.
Solution:
We know that

Thus, average run scored = 43.9 runs.

Question 5.
Calculate arithmetic mean of marks obtained in English in monthly test of 10 students
S.No. :                  1     2     3    4    5     6     7    8    9    10
Marks obtained : 30   28   32  12  18   20   25  15   26  14
Solution :

Thus, arithmetic mean = 22 marks

Question 6.
The number of books issued to students in 10 days from library of a school are as follows :
300   405   455    489    375     280    418    502    300     476
Find the average books issued daily.
Solution :
Arithmetic mean

Thus, average books issued daily = 400 books.

Question 7.
The average weight of 25 students of group A of a class is 51 kg. Whereas average weight of 35 students of group B is 54 kg. Find the average weight of 60 students of this class.
Solution :
Average weight of 25 students of group A = 51 kg
Thus, total of weight of 25 students
W1 = 51 x 25 = 1275 kg
Average weight of 35 students of group B = 54 kg
Thus, sum of weight of 35 students, W2 = 54 x 35 = 1890 kg
∴ Average weight of 60 students of class
= 
=  = 52.75 kg
Thus, average wt. of 60 students = 52.75 kg

Question 8.
The average of 5 numbers is 18, if one number is removed, then average becomes 16. Find the removed number.
Solution :
Sum of 5 numbers = 18 × 5 = 90
Let removed number is x
Then, sum of four number = 16 × 4 = 64
⇒ Sum of four number + x = 90
⇒ 64 + x = 90
x = 90 – 64 = 26
Thus, fifth number = removed number = 26

Question 9.
The mean of 13 numbers is 24. If 3 is added to each number, then what will the new mean?
Solution :
According to question,
Mean of 13 numbers = 24
Let 13 nos. are x1, x2, ….., x13
∵ Arithmetic mean

Thus, new mean will be (24 + 3) = 27.

Question 10.
The average monthly salary of five employees of a school is ₹3000. After retirement of one employee, average salary of remaining becomes ₹3200. What was the salary of fifth employee at the time of retirement ?
Solution :
Given : Average salary of 5 employees = ₹3000

⇒ Sum of salary of 5 employees = 3000 x 5 = ₹15000
Again, average salary of 4 employees = 3200
∵ Sum of salary of 4 employees = 3200 x 4 = ₹12800
Thus, salary of fifth employee = Sum of salary of 5 employees – Sum of salary of 4 employees
= ₹15000 – ₹12800 = ₹2200