Question

Find the median of data 30,25,32,23,42,36,40,33,21,43

Answer 1

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Answer 2

Given,

30,25,32,23,42,36,40,33,21,43

To Find,

The median =?

Solution,

It is asked that we have to find the median of the given data: 30,25,32,23,42,36,40,33,21,43.

The median of a given set of data is defined as the middle term of the set, in ascending order.

First, we will arrange the data in ascending order.

$Ascending\: order = 21, 23,25,30,32,33,36,40,42,43$

Now,

Since the number of values in the set is 10, i.e., even, the formula for finding the median is:

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

Where, $n = Total\: number\: of\: values\: in\: the\: set$

Here, $n =10$

Substituing n = 10 in the above formula,

$Median\: = \frac{(\frac{10}{2})^{th}\: term + (\frac{10}{2} + 1)^{th}\: term}1$

$Median\: = \frac{(5)^{th}\: term + (5 + 1)^{th}\: term}1$

$Median\: = \frac{(5)^{th}\: term + (6)^{th}\: term}1$

In the given set arranged in ascending order, the 5th term is 32 and the 6th term is 33.

Therefore,

$Median = \frac{32 + 33}{2}$

$Median = 32.5$

Hence, the median of the data is 32.5.