If mean of the data 5, 6, 8, 13, p+3, 8, 3 is 7 and its median is q,…

The correct answer is Option (1) → 3

The mean (sum ÷ number of values) gives p; the median is the middle value once the data are arranged in order.

Finding p (mean 7, seven values):

• Sum \(=5+6+8+13+(p+3)+8+3=46+p\)

• \(\displaystyle\frac{46+p}{7}=7\), so \(46+p=49\) and \(p=3\)

Finding q (the fifth value, p + 3, is 6):

• In order: 3, 5, 6, 6, 8, 8, 13

• The middle (4th) value is 6, so \(q=6\)

So \(\sqrt{p+q}=\sqrt{3+6}=\sqrt{9}=3\).