Question

The heights and inches of six basketball players at a local high school are given as a Dataset

70 78 74 82 60 75

Find the range and the interquartile range of the dataset

Answer 1

To find the range of the dataset, we need to subtract the smallest value from the largest value:

Range = 82 - 60 = 22

The interquartile range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1). To find the quartiles, we first need to arrange the dataset in increasing order:

60, 70, 74, 75, 78, 82

The median (Q2) of the dataset is the average of the two middle numbers, which in this case are 74 and 75. Therefore, Q2 = (74 + 75) / 2 = 74.5.

To find Q1 and Q3, we split the dataset into two halves:

1st half: 60, 70, 74
2nd half: 75, 78, 82

Q1 is the median of the 1st half, which is 70. Q3 is the median of the 2nd half, which is 78.

Therefore, Q1 = 70 and Q3 = 78.

Now, we can calculate the IQR:

IQR = Q3 - Q1 = 78 - 70 = 8

The range of the dataset is 22 and the interquartile range (IQR) is 8.