Question

The following stemplot displays the weights (in pounds) of a random sample of 20 men. What is the interquartile range of this data?

Men's Weights
13 26
14 18
15 289
16 477 Stem =tens
17 136 leaf = onch
18
19 019
20 2269

a. 40 pounds
b. 33 pounds
c. 47 pounds
d. 77 pounds
e. 16.5 pounds

Answer 1

The interquartile range (IQR) of the given stemplot data is 49 pounds, which is the difference between the third and first quartile values.

Step-by-step explanation:

Reading the given stemplot, we can determine the interquartile range (IQR) by finding the weights that correspond to the first (Q1) and third quartiles (Q3). Since there are 20 data points, Q1 is the 5.5th data point (the average of the 5th and 6th data points), and Q3 is the 15.5th data point (the average of the 15th and 16th data points).

Q1 is the average of the 5th (weight of 155) and 6th (weight of 158) weights, which is (155+158)/2 = 156.5 pounds. Q3 is the average of the 15th (weight of 202) and 16th (weight of 209) weights, which is (202+209)/2 = 205.5 pounds. The interquartile range is therefore Q3 - Q1 = 205.5 - 156.5 = 49 pounds.

Answer 2

The interquartile range of the data is 3.2 pounds.

Step-by-step explanation:

The interquartile range (IQR) is a measure of the spread of the middle 50% of the data. To find the IQR, we first need to find the lower quartile (Q1) and the upper quartile (Q3). In this case:

Q1 = 16 + (17/10) = 16.7

Q3 = 19 + (19/10) = 19.9

Then, the IQR = Q3 - Q1 = 19.9 - 16.7 = 3.2 pounds. Therefore, the interquartile range of the data is 3.2 pounds.