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Do you like to garden?
The heights (in centimetres) of plants in a garden are:
22, 26, 30, 34, 39, 43, 48, 51
How could we find the interquartile range?
The interquartile range measures the spread of the middle 50% of the data.
Where is the middle 50% of the data?
Between the lower and the upper quartile!
Let's recall that quartiles divide the data into quarters:
Lower quartile = 1st quartile (Q1) = 25th percentile, i.e. value that 25% (one quarter) of the data are smaller or equal to
Median = 2nd quartile (Q2) = 50th percentile, i.e. value that 50% (two quarters) of the data are smaller or equal to
Upper quartile = 3rd quartile (Q3) = 75th percentile, i.e. value that 75% (three quarters) of the data are smaller or equal to
Since Q1 is 1/4 of the way through the data and we have 8 data points in total, the lower quartile will be at:
(8 + 1) ÷ 4 = 2.25th position
But there is no 2.25th position - only the 2nd and the 3rd numbers!
When this happens, we just take the mean of the 2nd and the 3rd numbers, i.e. 26 and 30:
Q1 = (26 + 30) ÷ 2 = 28
Similarly, the upper quartile is 3/4 of the way through the data so it is at the 3 x (8 + 1) ÷ 4 = 6.75th position.
So the upper quartile is the mean of the 6th and 7th numbers:
Q3 = (43 + 48) ÷ 2 = 45.5
The interquartile range (IQR) is then the difference between the upper and the lower quartile:
IQR = Q3 - Q1 = 45.5 - 28 = 17.5
So the middle 50% of the data is spread out over 17.5 cm!
Ready to have a go at some questions?
