Question

Find the median for the following data.

$$\begin{array}{cccccc}Observation& 3& 6& 7& 9& 10\\ Frequency& 8& 10& 15& 9& 8\end{array}$$

• A. 3
• B. 6
• C. 7
• D. 9

Answer 1

The correct option is C 7

Sum of frequency is 50 or $\sum f_i$ = 50 and calculate less than cumulative frequencies in the table.

observation$\left(x_i\right)$ frequency$\left(f_i\right)$ cumulative frequency$\left(c{f}_i\right)$

3	8	8
6	10	18
7	15	33 (Median Class)
9	9	42
10	8	50
	$\sum f_i$=50

Since, even number of observation so the median will be the average of
$(\frac{n}{2}{)}^{th}$ = $(\frac{50}{2}{)}^{th}$ observation and $(\frac{n}{2}+1{)}^{th}$ = $(\frac{50}{2}+1{)}^{th}$ observation i.e., average of ${25}^{th}$ and ${26}^{th}$ observations repectively.

The first 8 observations occurs 3 times, next 10 occurs times and next 15 occurs 7 times.

So, the ${25}^{th}$ and ${26}^{th}$ observation will be 7 and 7 respectively.

Average of 7 and 7 = $\frac{7+7}{2}$ = 7
Thus, median of the given data is 7.