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If the median of the data 13, 17, (p + 1), (p + 5), 24, 27 is 21, then p is equal to :
1. 18
2. 19
3. 21
4. 23

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Correct Answer - Option 1 : 18

Concept used:

Median: The middle number; found by ordering all data points and picking out the one in the middle (or if there are two middle numbers, taking the mean of those two numbers).

Formula used:

The median formula of a given set of numbers, say having 'n' odd number of observations, can be expressed as:
Median = [(n + 1)/2]th term

The median formula of a given set of numbers say having 'n' even number of observations, can be expressed as:
Median = [(n/2)th term + ((n/2) + 1)th term]/2

Calculation:

Data is 13, 17, (p + 1), (p + 5), 24, 27 and their median is 21.

Number of terms is 6.

⇒ Median = [(p + 1) + (p + 5)]/2

⇒ 21 × 2 = 2p + 6

⇒ 42 = 2p + 6

⇒ 2p = 36

⇒ p = 18

∴ The value of p is 18.

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