Question

d. how many boys had a pulse rate of at most 82?

1. the height’s of 20 basketball players, in inches, are given below.

68, 70, 70, 71, 75, 80, 81, 82, 84, 75
75, 80, 75, 77, 75, 80, 83, 80, 71, 70

a) make a dot plot using the number line below.

68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84

b) what is the spread (range) of the data?

c) what is the mode of the data?

d) how many players are greater than 70 inches tall?

Explanation:

Part a)

Step1: Count occurrences

First, we count how many times each height appears:

• 68: 1
• 70: 3 (from 70, 70, 70)
• 71: 2 (from 71, 71)
• 75: 5 (from 75, 75, 75, 75, 75)
• 77: 1
• 80: 4 (from 80, 80, 80, 80)
• 81: 1
• 82: 1
• 83: 1
• 84: 1
• 69, 72, 73, 74, 76, 78, 79: 0

Step2: Draw dots

For each height on the number line, we place dots equal to their count:

• Above 68: 1 dot
• Above 70: 3 dots
• Above 71: 2 dots
• Above 75: 5 dots
• Above 77: 1 dot
• Above 80: 4 dots
• Above 81: 1 dot
• Above 82: 1 dot
• Above 83: 1 dot
• Above 84: 1 dot
• Above 69, 72, 73, 74, 76, 78, 79: 0 dots

(Note: Since we can't draw the actual dot - plot here, this is the process to create it. The number line is as given: 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84)

Part b)

Step1: Identify max and min

The range is calculated as \( \text{Range}=\text{Maximum value}-\text{Minimum value} \).
From the data set, the minimum value is 68 (the smallest height) and the maximum value is 84 (the largest height).

Step2: Calculate range

Using the formula for range, we have \( \text{Range}=84 - 68=16 \).

Step1: Recall mode definition

The mode is the value that appears most frequently in a data set.

Step2: Find most frequent value

From the counts in part a), the height 75 appears 5 times, which is more frequent than any other height (70 appears 3 times, 80 appears 4 times, etc.).

Answer:

The spread (range) of the data is 16.

Part c)