Question

If the mode of the following distribution is 57.5 find the value of x
Class Interval 30-40 40-50 50-60 60-70 70-80 80-90 90- 100
Frequency 6,10, 16,x,10,5,2

Answer 1

The value of "x is equal to 14".

Step-by-step explanation:

The given table:

Class         Frequency

30-40         6

40-50        10

50-60        16

60-70        x

70-80       10

80-90       5

90-100      2

Here, the maximum class frequency is 16 and corresponding to this frequency is 50-60.

The modal class = 50 - 60

∴ Mode $=x_{k} +(\dfrac{f_{k}-f_{k-1}}{2f_{k}-f_{k-1}-f_{k+1}}) \times h$

⇒$50+(\dfrac{16-10}{2(16)-10-x}) \times 10=57.5$

⇒$(\dfrac{6}{22-x}) \times 10=57.5-50$

⇒$\dfrac{60}{7.5}=22-x$

⇒$22-x=8$

⇒ x =22 - 8 = 14

Hence, the value of "x is equal to 14".

Answer 2

ANSWER: x=14

as 60/7.5= 22-x

22-x = 8

as , x= 8-22

x=14 ( Final Answer)