Question

Calculate the mean and the median for the following distribution:
Number 5 10 15 20 25 30 35
Frequency 1 2 5 6 3 2 1​

Answer 1

Given:

Numbers 5, 10, 15,20, 25, 30, and 35 have frequencies 1, 2, 5,6,3, 2, and 1​ respectively.

To Find:

Mean and the median for the following distribution

Solution:

(i) Calculation of mean

Mean of grouped data is given by the formula:

Mean = ∑fx / ∑f..........(a)

where 'f' represents frequencies and 'x' represents variates

For the given distribution,

∑fx = [(5x1) +(10x2) + (15x5) + (20x6) + (25x3) + (30x2) + (35x1)] = 390

∑f = ( 1 +2+ 5+ 6+ 3+ 2+ 1​) = 20

Putting the values in eq(a), we get

Mean = (390/20) = 19.5

(ii) Calculation of Median

Since 7 observations are given ⇒ (n =7),which is an odd number

So, median will be calculated by the formula,

$Median = (\frac{n +1}{2}th)term$

$Median = (\frac{7 +1}{2}th)term$

⇒ 4th term = 20

Hence, the mean of the given observation is 19.5 and the median is 20