Question

Which data set is represented by the modified box plot?

Box and whisker plot on a number line from 90 to 160 in increments of 5. The whisker ranges from 100 to 126. The box ranges from 109 to 124 with the vertical bar inside the box at 117. One dot mark above one hundred and fifty-one.


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Responses

a 114, 114, 116, 117, 118, 122, 124, 126, 151
a 114, 114, 116, 117, 118, 122, 124, 126, 151

b 104, 104, 116, 117, 118, 124, 136, 142, 151
b 104, 104, 116, 117, 118, 124, 136, 142, 151

c 104, 104, 106, 107, 108, 124, 126, 132, 151
c 104, 104, 106, 107, 108, 124, 126, 132, 151

d 100, 104, 114, 116, 117, 118, 122, 126, 151

Answer 1

To interpret the modified box plot, let's analyze the given information:

1. **Whiskers**:
- The lower whisker ends at 100.
- The upper whisker ends at 126.

2. **Box**:
- The left side of the box is at 109.
- The right side of the box is at 124.
- The median (indicated by the vertical bar inside the box) is at 117.

This means:
- The minimum value in the data set is 100.
- The lower quartile (Q1) is 109.
- The median (Q2) is 117.
- The upper quartile (Q3) is 124.
- The maximum value (the last data point, beyond the whiskers) is 151.

Now, let's look at the options to see which one fits these statistics:

a. **114, 114, 116, 117, 118, 122, 124, 126, 151**
- Min = 114 (not 100), exceeds the minimum whisker.

b. **104, 104, 116, 117, 118, 124, 136, 142, 151**
- Min = 104 (not 100), exceeds the minimum whisker.

c. **104, 104, 106, 107, 108, 124, 126, 132, 151**
- Min = 104 (not 100), exceeds the minimum whisker.

d. **100, 104, 114, 116, 117, 118, 122, 126, 151**
- Min = 100 (matches).
- Q1 = 104.
- Median = 117.
- Q3 = 126.
- Max = 151.

The only data set that matches the criteria indicated by the box plot is:

**d: 100, 104, 114, 116, 117, 118, 122, 126, 151**.