Answer:
- The statement that is true is the last one: The data set for box plot 2 has a larger interquartile range than the data set for box plot 1.
Explanation:
In a box plot the following statistics are shown:
- Minimum value: it is the extreme point far to the left
- First quartile (Q1): it is the first vertical line of the box to the left
- Median or secong quartile (Q2): it is the vertical line inside the box
- Third quartile (Q3): it the last vertical line of the box (the farthest to the right)
- Maximum value: it is the extreme point far to the right
From that you can calculate the range and the interquartile range:
- Range = maximum value - minimum value
- Interquartile range = Q3 - Q1
With that you can analyze the two data set:
FIRST STATEMENT:
The mode of the data set for box plot 1 is greater than the mode of data set for box plot 2.
FALSE: you cannot conclude anything about the mode because a box plot does not indicate the mode.
SECOND STATEMENT:
The data set for box plot 1 has a larger range than the data set for box plot 2.
FALSE
Range of data set for box plot 1 is:
- Min ≈ 25
- Max ≈ 45
- Range = Max - Min ≈ 45 - 25 ≈ 20
Range of data set for box plot 2 is:
- Min = 20
- Max = 50
- Range = Max - Min = 50 - 20 = 30
THIRD STATEMENT:
The data set for box plot 2 has a higher median than the data set for box plot 1.
FALSE
- Median of data set for blog pot 2 (Q2) = 30
- Median of data set for blog pot 1 (Q2) ≈ 36
FOURTH STATEMENT:
The data set for box plot 2 has a larger interquartile range than the data set for box plot 1.
TRUE
- Interquartile range of data set for box plot 2: Q3 - Q1 = 40 - 25 = 15
- Interquartile range of data set for box plot 1: Q3 - Q1 ≈ 42 - 33 ≈ 9
