Question

If mode of the following series is 54,find of f. Class intervals:0-15, 15-30, 30-45, 45-60, 60-75, 75-90. Frequencies are 3,5,f, 16,12,7.

Answer 1

The value of f is 10.

Explanation:

Given table:

Class intervals   Frequency

0-15                               3

15-30                             5

30-45                             f

45-60                             16

60-75                              12

75-90                                7

Formula for mode = $l+(\dfrac{f_1-f_0}{2f_1-f_0-f_2})\times h$

, where h= class width

l= lower limit of modal class.

$f_1$ = frequency corresponding to modal class.

$f_o$ = frequency preceding to modal class.

$f_2$ = frequency proceeding to modal class.

Since mode is 54 which lies in class 45-60 , so l= 45 , h= 60-45=15 , $f_1=16$  , $f_0=f$ and $f_2=12$.

Put all values in formula , we get

$54=45+(\dfrac{16-f}{2(16)-f-12})\times (15)$

$54-45=(\dfrac{16-f}{32-f-12})\times (15)$

$9=(\dfrac{16-f}{20-f})\times (15)$

$9(20-f)=15(16-f)$

$180-9f=240-15f$

$-9f+15f=240-180$

$6f=60\Rightarrow\ f=10$

Hence, the value of f is 10.

# Learn more :

Find the mode of 90,55,67,55,75,75,40,35,55,95

https://brainly.in/question/7442631

Answer 2

Answer:

this is the answer for ur question

Step-by-step explanation:

hope it helps u