To find the range, we subtract the smallest value from the largest value.
Range = 78 - 38 = 40
Now, in order to find the interquartile range, we first need to find the first quartile (Q1) and the third quartile (Q3). Q1 is the median of the first half of the data, and Q3 is the median of the second half of the data.
Arranging the temperatures in increasing order: 38, 70, 72, 74, 75, 78, 78
Q1 = (72 + 74)/2 = 73
Q3 = (74 + 75)/2 = 74.5
Interquartile Range = Q3 - Q1 = 74.5 - 73 = 1.5
The interquartile range is the best measure of variability for these values because it is not affected by extreme values like the range is. In this case, the range of 40 is largely influenced by the extreme low temperature of 38 degrees on Friday. On the other hand, the interquartile range of 1.5 only considers the middle 50% of the data, making it a more reliable measure of variability.
The following temperatures are expected over the next week. On Wednesday it will be 78 degrees, on Thursday it will be 75 degrees, on Friday it will be 38 degrees, on Saturday it will be 74 degrees, on Sunday it will be 70 degrees, on Monday it will be 72 degrees, and finally on Tuesday it will be 78 degrees. Use these numbers to find the Range and Interquartile Range. Explain why the Interquartile Range is the best measure of variability for these values.
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