A researcher wants to know what people in Melbourne think about football. She asks ten people to rate their attitude towards football on a scale from 0 (don't like football at all) to 10 (like football a lot). The ratings are as follows: 10, 9, 6, 9, 5, 5, 1, 5, 10, 6 What is the interquartile range (IQR) of this data?

Question

A researcher wants to know what people in Melbourne think about football. She asks ten people to rate their attitude towards football on a scale from 0 (don't like football at all) to 10 (like football a lot). The ratings are as follows: 10, 9, 6, 9, 5, 5, 1, 5, 10, 6  What is the interquartile range (IQR) of this data?

BlackTom AI · Accepted Answer

We start by listing the data: 10, 9, 6, 9, 5, 5, 1, 5, 10, 6.
Next, sort the data in ascending order: 1, 5, 5, 5, 6, 6, 9, 9, 10, 10.
There are 10 observations (an even number), so the median is between the 5th and 6th values, but for quartiles we typically divide the data into a lower half and an upper half.
Lower half (first 5 values): 1, 5, 5, 5, 6. The median of this lower half is the third value, which is 5. This gives Q1 = 5.
Upper half (last 5 values): 6, 9, 9, 10, 10. The median of this upper half is the third value, which is 9. This gives Q3 = 9.
The interquartile range (IQR) is Q3 minus Q1, which is 9 − 5 = 4. However, the question seems to present IQR as the interval defined by Q1 and Q3, i.e., (Q1, Q3).
With Q1 = 5 and Q3 = 9, the corresponding option should reflect (5, 9).
Now evaluate the answer choices:
- a. 6, 6: This would imply Q1 = 6 and Q3 = 6, which contradicts the calculated quartiles since the lower half’s median is 5 and the upper half’s median is 9.
- b. 5, 6: This would imply Q3 = 6, but the upper half’s median is 9, not 6.
- c. 6, 9: This would imply Q1 = 6, which is not supported by the lower half’s median of 5.
- d. 5, 9: This matches Q1 = 5 and Q3 = 9 derived from the data.
Thus, the pair that corresponds to the data’s quartiles is (5, 9).

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