Question

An incomplete distribution is given below:
variable: 10-20 20-30 30-40 40-50 50-60 60-70 70-80
Frequency: 12 30 - 65 - 25 18
You are given that the median value is 46 and the total number of items is 230.
(i) Using the median formula fill up missing frequencies.
(ii) Calculate the AM of the completed distribution.

Answer 1

(i) Missing frequencies = 34 and 46.

(ii) Arithmetic mean = 45.87.

Given:

    Variable : 10-20 20-30 30-40 40-50 50-60 60-70 70-80

Frequency : 12 30 - 65 - 25 18

Median value is 46

Total number of items is 230

To find:

Missing frequencies?      

Arithmetic mean?

From the given data:

(i) Using the median formula filling up the missing frequencies :

Let missing frequency be x  and y

See the table below attached.

The given median = 46

The median class is 40-50

Lower frequency (L) = 40, Difference(h) = 10, N=230, f=65 and cf=42+x

$\text{Median} =\text{ L }+ (\frac{\frac{\text{N}}{2} - \text{cf}}{\text{f}} ) \times \text{h}$

By putting the value and solving above equation we get x = 34.

Total number of items is,

230 = 12 + 30 + x + 65+ y + 25 + 18                                        

230 = 150+x+y                                  

         y = 46

(ii) Calculating the AM - Arithmetic Mean of the completed distribution :

From second table,            

AM = $\frac{\sum \mathrm{fx} }{\text{N}}$

       = $\frac{10550}{230}$

       = 45.87

Therefore, Arithmetic Mean is 45.87.

To learn more....

1. The following is the distribution of height of students of certain class in a certain city: Find the average height of maximum number of students.

Height(in cms): 160-162 163-165 166-168 169-171 172-174

No.of students: 15 118 142 127 18

brainly.in/question/15924910

2. The following is the distribution of height of students of certain class in a certain city: Find the average height of maximum number of students.

Height(in cms): 160-162 163-165 166-168 169-171 172-174

No.of students: 15 118 142 127 18

brainly.in/question/15924910