The diagram shows twelve cards. Each card has a number printed on it. (a) Find the median of the numbers on the cards. [2] (b) Work out the range of the num...
Question 1 Report
The diagram shows twelve cards. Each card has a number printed on it.
(a) Find the median of the numbers on the cards. [2]
(b) Work out the range of the numbers on the cards. [1]
Answer Details
Both parts need the numbers arranged in order of size, so ordering the twelve card values is the first move in either case.
(a) In order the numbers are
\[ 3,\ 5,\ 7,\ 8,\ 9,\ 11,\ 12,\ 14,\ 15,\ 19,\ 22,\ 27 \][M1] for the correct ordered list, or for identifying the middle pair. With twelve values, \(\frac{12+1}{2}=6.5\), so the median lies halfway between the \(6\)th and \(7\)th values, which are \(11\) and \(12\):
\[ \text{median}=\frac{11+12}{2}=11.5 \][A1].
(b) The range is the largest value minus the smallest:
\[ 27-3=24 \][B1].
With an even number of values the median usually is not one of the data values, and \(11.5\) is not printed on any card. That is correct and expected. The frequent error is taking a single "middle" card from the unordered display, or averaging the \(5\)th and \(8\)th values; the two central positions must be counted from the ordered list.
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