Page 11 - Lesson note-5-Ch 14 Statistics ( Measure of Central Tendency)

It can be written as
(2x + 10 + 2x - 8)/2 = 25
4x + 2 = 50
4x = 48
x = 12
Therefore, the value of x is 12.

Question 7.
Find the mode of the following items.
0, 6, 5, 1, 6, 4, 3, 0, 2, 6, 5, 6
Solution:
By arranging the numbers in ascending order
We get
0, 0, 1, 2, 3, 4, 5, 5, 6, 6, 6, 6
Observations (x) 0 1 2 3 4 5 6
Frequency 2 1 1 1 1 2 4
From the table we know that 6 occurs maximum number of times so the mode is 6.

Question 8.
If the mean of the data 3, 21, 25, 17, (x + 3), 19, (x – 4) is 18, find the value of x. Using
this value of x, find the mode of the data.
Solution:
We know that
Number of observations = 7
It is given that mean = 18
It can be written as
(3 + 21 + 25 + 17 + x + 3 + 19 + x – 4)/7 = 18
2x + 84 = 126
2x = 42
x = 21
By substituting the value of x
(x + 3) = 21 + 3 = 24
(x – 4) = 21 – 4 = 17
So we get
3, 21, 25, 17, 24, 19, 17
We know that 17 occurs maximum number of times so the mode is 17.

Question 9.
The numbers 52, 53, 54, 54, (2x + 1), 55, 55, 56, 57 have been arranged in an
ascending order and their median is 55. Find the value of ‘x’ and hence find the mode of
the given data.
Solution:
We know that Number of observations = 9
By arranging the numbers in ascending order
We get
52, 53, 54, 54, (2x + 1), 55, 55, 56, 57