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

We start by listing the given weights in ascending order to prepare for quartile calculation: 51, 51.5, 52, 52, 53, 53, 53, 54, 55, 57, 57, 60.
Since there are 12 data points (an even number), we split the data into two halves of 6 values each to determine Q1 and Q3.
Lower half (first 6 values): 51, 51.5, 52, 52, 53, 53. The median of this half is the average of its 3rd and 4th values, which are 52 and 52. Therefore, Q1 = 52.
Upper half (last 6 values): 53, 54, 55, 57, 57, 60. The median of this half is the average of its 3rd and 4th values, which are 55 and 57. Therefore, Q3 = (55 + 57) / 2 = 56.
The interquartile range (IQR) is Q3 − Q1, which equals 56 − 52 = 4.
Note on alternative definitions: some approaches define quartiles differently (for example, using a different method for locating quartile boundaries or including/excluding the median in halves), and those methods can yield a different IQR, such as 3.5. Here, the commonly taught method of splitting the data into two equal halves and taking the medians of those halves leads to an IQR of 4.

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)简答题

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