Question

An incomplete distribution is given below:Variable You are given that the median value is 70 and the total number of items is 200. Using the median formula fill up the frequencies.

Answer 1

Answer:

The missing frequencies are x = 8 and y = 43.

Step-by-step explanation:

Median Value =70

Then the median Class =60-80

Let the missing frequencies be x and y.

Given: Total Frequncy = 200 , Median = 46

$\left|\begin{array}{c|ccccccc}Value&0-20&20-40&40-60&60-80&80-100&100-120&120-140\\Frequency&12&30&x&66&y&27&14\\ Cumu.Freq&12&42&42+x&108+x&108+x+y&135+x+y&149+x+y\end{array}\right|$

From the table

$\sum f_i =149+x+y$  

Here, n = 200

n/2 = 100

Lower Class Boundary of the median class, l=60

Frequency of the median class(f) =66

Cumulative Frequency before the median class, f=42+x

Class Width, h=10

$Median = l + \dfrac{\dfrac{n}{2} - c.f }{f} \times h$

$70 = 60+ \dfrac{100- 42+x }{66}\times 10\\70 = 60+ \dfrac{58+x }{66}\times 10\\70-60=\dfrac{58+x }{66}\times 10\\10*66=10(58+x)\\58+x=66\\x=66-58\\x=8$

200=149+x+y

200=149+8+y

y=200-(149+8)

y=43

Hence, the missing frequencies are x = 8 and y = 43.