Here are five numbers. \(12\qquad 7\qquad 12\qquad 9\qquad 15\) (a) Work out the mean. [1] (b) Write down the median. [1] (c) Work out the range. [1]
Question 1 Report
Here are five numbers.
\(12\qquad 7\qquad 12\qquad 9\qquad 15\)
(a) Work out the mean. [1]
(b) Write down the median. [1]
(c) Work out the range. [1]
Answer Details
Mean, median and range are three different summaries of the same five numbers \(12\), \(7\), \(12\), \(9\), \(15\), and only the median needs the numbers put in order.
(a) The mean is the total divided by how many numbers there are:
\[ \frac{12+7+12+9+15}{5}=\frac{55}{5}=11 \]The mean is \(11\). [B1]
(b) In order the numbers are \(7,\ 9,\ 12,\ 12,\ 15\). With five values the median is the \(3\)rd, so the median is \(12\). [B1]
(c) The range is the largest minus the smallest:
\[ 15-7=8 \]The range is \(8\). [B1]
The single most common error is reading the median straight off the unsorted list, which would give \(12\) here by luck but fails in general. Always sort first. Note too that the mean and median differ, \(11\) against \(12\), because the low value \(7\) drags the mean down while leaving the middle value untouched.
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