Question

The Following data shows the goals scored by 19 clubs in a Premiere League Season :

$\begin{array}{cc}\text{Goals Scored}& \text{No. of Clubs}\\ 0-10& 2\\ 10-20& 3\\ 20-30& 2\\ 30-40& 4\\ 40-50& 3\\ 50-60& 5\end{array}$

Find the Median number of Goals scored in the season.

Answer 1

The Cumulative frequency table of the data is given as :

$\begin{array}{cc}\text{Goals Scored}& \text{No. of Clubs(Cumulative)}\\ <10& 2\\ <20& 5\\ <30& 7\\ <40& 11\\ <50& 14\\ <60& 19\end{array}$

N = 19 (An odd number)

Median = $\frac{(19+1)}{2}th$ observation = 10th observation.

So, the Median class is 30 - 40

We know that there are 4 observations from the 7th observation to the 11th observation which come between 30 and 40.

However, we do not know their individual goals.

We will divide 10 from 30 to 40 into 4 equal parts and assume that one observation is in each subdivision.

We will assume that the value of each observation in a subdivision is the mid - value of the subdivision.

So, the the value of the 8th observation is the mid value of 30 and $30\frac{10}{4}$ft, that is $30\frac{10}{8}$

So, from the 8th observation to the 10th observation, there are 2 observations.

If the 8th term of the AP is $30\frac{10}{8}$ and the common difference is $\frac{10}{4}$,

Then the 10th term = $30\frac{10}{8}$ + $2\times \frac{10}{4}$

= $30+\frac{10+40}{8}$

= 30 + 6.25

= 36.25