The weights (in kg) carried by the horses in a handicap race are given below. 60 57 57 55 54 53 53 53 52 52 51.5 51 What is the interquartile range? (Write the value only, don't include the units)

Question

BlackTom AI · Accepted Answer

The task provides a data set of weights and asks for the interquartile range (IQR). 
First, note the data are: 60, 57, 57, 55, 54, 53, 53, 53, 52, 52, 51.5, 51.
Sort the data in ascending order to identify quartiles more easily: 51, 51.5, 52, 52, 53, 53, 53, 54, 55, 57, 57, 60.
With 12 data points (an even count), the median lies between the 6th and 7th values, but for IQR we need Q1 and Q3.
- Q1 (the first quartile) is the median of the first half of the data (the first 6 values): 51, 51.5, 52, 52, 53, 53. The middle of these is the average of the 3rd and 4th values: (52 + 52) / 2 = 52.
- Q3 (the third quartile) is the median of the second half of the data (the last 6 values): 53, 54, 55, 57, 57, 60. The middle of these is the average of the 3rd and 4th values: (55 + 57) / 2 = 56.
Now compute the interquartile range: IQR = Q3 − Q1 = 56 − 52 = 4.
Therefore, the interquartile range for this data set is 4. 
If you were checking the process, you’d verify each step by counting positions carefully and ensuring you used the correct halves for Q1 and Q3 in an even-sized data set.

The weights (in kg) carried by the horses in a handicap race are given below. 60 57 57 55 54 53 53 53 52 52 51.5 51 What is the interquartile range? (Write the value only, don't include the units)

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The weights (in kg) carried by the horses in a handicap race are given below. 60 57 57 55 54 53 53 53 52 52 51.5 51 What is the interquartile range? (Write the value only, don't include the units)

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