Question

Charlotte recorded the number of minutes she spent exercising in the past ten days: 10, 13, 5, 2, 9, 1, 14, 3, 5, 7. Find the median of the data.

Answer 1

Answer :-

To find median, we first need to aarange them in ascending order :-

10, 13, 5, 2, 9, 1, 14, 3, 5, 7.

Ascending order. - 1 , 2 , 3 , 5 , 5 , 7 , 9 , 10 , 13 , 14

As, number of terms are even -

$\implies\sf Median = \dfrac{\left(\dfrac{n}{2} \right)^{th} + \left(\dfrac{n}{2} + 1 \right)^{th} \: observation}{2}$

Here,

• n = 2

$\implies\sf Median = \dfrac{\left(\dfrac{10}{2} \right)^{th} + \left(\dfrac{10}{2} + 1 \right)^{th} \: observation}{2}$

$\implies\sf Median = \dfrac{5^{th} + 6^{th} \: observation}{2}$

• 5th observation = 5
• 6th observation = 7

$\implies\sf Median = \dfrac{5 + 7}{2}$

$\implies\sf Median = \dfrac{12}{2}$

$\implies\sf Median = 6$

Hence, median of data is 6