Question

100 students record how far they can run in one minute.

The results are shown in the table :

$\begin{array}{cc}\text{Distance(d metres)}& \text{frequency}\\ 0-200& 5\\ 200-250& 20\\ 250-300& 50\\ 300-400& 25\end{array}$

Estimate the median.

• A. 285
• B. 275.5
• C. 245.75
• D. 322.5

Answer 1

The correct option is B

275.5

The cumulative frequency table can be given as :

$\begin{array}{cc}\text{Distance(d metres)}& \text{Cumulative frequency}\\ 0-200& 5\\ 200-250& 25\\ 250-300& 75\\ 300-400& 100\end{array}$

The median will be given by the average of the 50th and 51st observation

They both lie in the interval 250 - 300

Interval = 50

No. of students in this range = 50

50th Observation = 250 + 25 = 275

51st Observation = 250 + 26 = 276

Median = Average of 50th and 51st observation = $\frac{275+276}{2}=275.5$