GCSE Mathematics (9-1)
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    25.1 Quartiles, interquartile range and box plots — Practise with help

    Try each question before opening its hint. Reveal the working when you want to check.

    Warm-up: remember

    1. Order 4,9,2,7,54, 9, 2, 7, 5.
    2. Find the median of 3,6,8,10,123, 6, 8, 10, 12.
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    1. 2,4,5,7,92,4,5,7,9. 2. 88, the middle value.

    Practise with help

    1. Find the median, lower quartile and upper quartile of 2,4,5,7,8,10,12,142,4,5,7,8,10,12,14.

    Hint

    Split the ordered list into two equal halves. Find each half's median.

    Step

    The median is the mean of positions 4 and 5. The lower and upper halves each have four values.

    Full working

    Median =(7+8)/2=7.5=(7+8)/2=7.5. Lower quartile =(4+5)/2=4.5=(4+5)/2=4.5. Upper quartile =(10+12)/2=11=(10+12)/2=11.

    2. Calculate the IQR for the data in question 1.

    Hint

    Subtract the lower quartile from the upper quartile.

    Step

    Use Q3−Q1=11−4.5Q_3-Q_1=11-4.5.

    Full working

    The IQR is 11−4.5=6.511-4.5=6.5.

    3. Earlier work: find the range of −3,2,6,9-3, 2, 6, 9.

    Hint

    Range means maximum minus minimum.

    Step

    Calculate 9−(−3)9-(-3).

    Full working

    The range is 9−(−3)=129-(-3)=12.

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