Question

The data has been arranged in ascending order: 14, 19, 25, 29, x, 39, 41, 48, 54. If the median of the data is 35. Find x.

Answer 1

Given: The set of observations (in ascending order); median being 35.

To find: The value of x.

Answer:

Observations: 14, 19, 25, 29, x, 39, 41, 48, 54.

Formula to find the median:

• $\sf \bigg(\dfrac{n\ +\ 1}{2}\bigg)th\ term,\ for\ when\ the\ number\ of\ observations\ is\ an\ odd\ number.$
• $\sf \bigg(\dfrac{n}{2}\bigg)th\ +\ \bigg(\dfrac{n}{2}\ +\ 1\bigg)th\ term,\ for\ when\ the\ number\ of\ observations\ is\ an\ even\ number.$

In this case, the number of observations (n) = 9, the first formula will be used.

Equating the reespective values:

$\sf 35\ =\ \bigg(\dfrac{9\ +\ 1}{2}\bigg)th\ term\\\\\\\sf 35\ =\ \bigg(\dfrac{10}{2}\bigg)\sf th\ term.\\\\35\ =\ 5th term.$

5th term = x.

Therefore, x = 5.