**How to find the median of a data set :**

Median is defined as the middle value of the data when the data is arranged in ascending or descending order.

Find the median of the following :

40, 50, 30, 60, 80, 70

Arrange the given data in ascending order.

30, 40, 50, 60, 70, 80.

Here the number of terms is 6 which is even. So the third and fourth terms are middle terms. The average value of the these terms is the median.

Median = (50 + 60)/2 = 110/2 = 55

(i) When the number of observations is odd, the middle number is the median.

(ii) When the number of observations is even, the median is the average of the two middle numbers.

**Example 1 :**

Find the median of the following data.

3, 4, 5, 3, 6, 7, 2.

**Solution :**

Arrange the data in ascending order.

2, 3, 3, 4, 5, 6, 7

The number of observation is 7 which is odd.

Hence the middle value 4 is the median.

**Example 2 :**

Find the median of the data

12, 14, 25, 23, 18, 17, 24, 20.

**Solution :**

Arrange the data in ascending order

12, 14, 17, 18, 20, 23, 24, 25

The number of observation is 8 which is even.

Median is the average of the two middle terms 18 and 20.

Median = (18 + 20) / 2

= 38/2

= 19

**Example 3 :**

Find the median of the first 5 prime numbers.

**Solution :**

The first five prime numbers are 2, 3, 5, 7, 11.

The number of observation is 5 which is odd.

Hence the middle value 5 is the median.

**Example 4 :**

Find the median of the following data.

6, 14, 5, 13, 11, 7, 8

**Solution :**

Arrange the data in ascending order

5, 6, 7, 8, 11, 13, 14

The number of observation is 7 which is odd.

Since the number of terms is odd, the middle term is the median.

Hence 8 is the median.

**Example 5 :**

The weight of 7 chocolate bars in grams are

131, 132, 125, 127, 130, 129, 133

Find the median.

**Solution :**

Arrange the data in ascending order

125, 127, 129, 130, 131, 132, 133

The number of observation is 7 which is odd.

Since the number of terms is odd, the middle term is the median.

Hence 130 is the median.

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