Consider the following dataset - HSC - SSCE Mathematics Standard - Question 28 - 2020 - Paper 1

The second set of data is: 1, 5, 9, 10, 15, x. Therefore, the mean is:

$\text{Mean}_{\text{second set}} = \frac{40 + x}{6}$

The median of the first set of data (1, 5, 9, 10, 15) is 9.

Since x > 15, the second set of data in order is: 1, 5, 9, 10, 15, x. The median is:

$\text{Median}_{\text{second set}} = 9.5$

According to the problem, the difference between the means is equal to ten times the difference between the medians:

$\frac{40 + x}{6} - 8 = 10(9.5 - 9)$

Simplifying gives:

$\frac{40 + x - 48}{6} = 10(0.5)$ $\frac{x - 8}{6} = 5$

Multiplying both sides by 6:

$x - 8 = 30$

Thus:

$x = 30 + 8 = 38$