**Median of ungrouped data examples :**

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

- When the number of observations is odd, the middle number is the median.
- 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.

17, 15, 9, 13, 21, 7, 32

**Solution :**

Arrange the data in ascending order.

7, 9, 13, 15, 17, 21, 32

The number of observation is 7 which is odd.

Hence the middle value 15 is the median.

**Example 2 :**

A cricket player has taken the runs 13, 28, 61, 70, 4, 11, 33, 0, 71, 92. Find the median.

**Solution :**

Arrange the runs in ascending order as 0, 4, 11, 13, 28, 33, 61, 70, 71, 92.

Here n = 10 (even number).

There are two middle values 28 and 33.

Median = Average of the two middle values

= (28 + 33) / 2 = 61/2 = 30.5

**Example 3 :**

Find the median of the following data.

83, 66, 86, 30, 81

**Solution :**

Arrange the data in ascending order.

30, 66, 81, 83, 86

The number of observation is 5 which is odd.

Hence the middle value 81 is the median.

**Example 4 :**

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 5 :**

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 6 :**

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 7 :**

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 8 :**

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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