Question

Data = 37, 41, 56, 62, 70, 74, 81, 89, 95 and 90.

Assertion (A): Median = 72.

Reason (R): If number of data(n) is odd, the median = `((n+1)/2)^(th)` term.

Options

• A is true, R is false.

• A is false, R is true.

• Both A and R are true and R is the correct reason for A.

• Both A and R are true and R is the incorrect reason for A.

Answer 1

Both A and R are true and R is the incorrect reason for A.

Explanation:

Given, data = 37, 41, 56, 62, 70, 74, 81, 89, 95 and 90.

Arrange the data in ascending order: 37, 41, 56, 62, 70, 74, 81, 89, 90, 95

Number of data = 10

If the number of data points (n) is odd, the median is the \[\left(\frac{n + 1}{2}\right)^{th}\] term

If the number of data points (n) is even, the median is the \[\left(\frac{\left(\frac{n}{2}\right)^{th} + \left(\frac{n}{2} + 1\right)^{th}}{2}\right)\]

Here, n = 10

\[\text{Median} = \left(\frac{\left(\frac{10}{2}\right)^{th} + \left(\frac{10}{2} + 1\right)^{th}}{2}\right)\]

\[{} = \left(\frac{5^{th} + (5 + 1)^{th}}{2}\right)\]

\[{} = \left(\frac{5^{th} + 6^{th}}{2}\right)\]

\[{} = \left(\frac{70 + 74}{2}\right)\]

\[{} = \left(\frac{144}{2}\right)\]

\[{} = 72\]

∴ Both A and R are true and R is incorrect reason for A.