Question

Given that the median value is 46,determine the missing frequencies using the median formula

Answer 1

hope so the answer is this.... if there is any kind of mistake then sorry.... but the process is this only....
thank you

Answer 2

The missing frequencies are $f_1=34, and f_2=45$.

Step-by-step explanation:

It is given that median of the data is 46.

Let $f_1=x, and f_2=y$

First find the cumulative frequency.

C.I              fi             c.f

10-20        12             12

20-30       30            42

30-40        x             42+x

40-50        65         107+x     ← Median class

50-60        y           107+x+y

60-70        25        132+x+y

70-80        18         150+x+y

Total        229

Using this table we get

$229=150+x+y$

$79=x+y$               .... (1)

Formula for median

$M=l+\dfrac{\frac{n}{2}-cf}{f}\times h$

l is lower limit of median class.

n is number of observations.

cf is the cumulative frequency of preceding the median class.

f is frequency of median class

h is class size.

Substitute M=46, l=40, n=229, cf=42+x, f=65 and h=10 in the above formula.

$46=40+\dfrac{\frac{229}{2}-(42+x)}{65}\times 10$

$46-40=\dfrac{114.5-42-x}{65}\times 10$

$6=\dfrac{72.5-x}{65}\times 10$

Divide both sides by 10.

$0.6=\dfrac{72.5-x}{65}$

Multiply both sides by 65.

$39=72.5-x$

$x=33.5$

The frequent can not be a decimal value. So, approximate the value to the whole number.

$x=34$

Substitute x=34 in equation (1).

$79=34+y$

$79-34=y$

$45=y$

Therefore, the missing frequencies are $f_1=34, and f_2=45$.

#Learn more:

The median of the following data is 525. Find the missing frequency, if it is given that there are 100 observation in the data:

https://brainly.in/question/7669599