The following are the ratings of men by women in an experiment involving speed dating. use the given data to construct a box plot and identify the 5 number summary. 2.0 2.5 3.5 4.5 4.5 4.5 5.0 5.0 5.0 5.0 5.5 6.5 6.5 6.5 6.5 7.0 8.0 8.0 8.0
To construct a box plot, we first need to order the data set in ascending order. So, the data set becomes:
2.0 2.5 3.5 4.5 4.5 4.5 5.0 5.0 5.0 5.0 5.5 6.5 6.5 6.5 6.5 7.0 8.0 8.0 8.0
The five-number summary consists of the minimum value, the first quartile (Q1), the median (Q2), the third quartile (Q3), and the maximum value.
First, let's find the minimum value, which is 2.0.
Next, let's find Q1. To calculate Q1, we need to find the median of the lower half of the data set. Since there are 19 data points, the median for the lower half would be the average of the 9th and 10th values.
The 9th value is 5.0, and the 10th value is 5.0. So Q1 = (5.0 + 5.0)/2 = 5.0.
The median (Q2) can be found by calculating the average of the 10th and 11th values.
The 10th value is 5.0, and the 11th value is 5.5. So Q2 = (5.0 + 5.5)/2 = 5.25.
To find Q3, we need to find the median of the upper half of the data set. Since there are 19 data points, the median for the upper half would be the average of the 15th and 16th values.
The 15th value is 7.0, and the 16th value is 8.0. So Q3 = (7.0 + 8.0)/2 = 7.5.
Finally, we find the maximum value, which is 8.0.
So, the five-number summary of the data set is: 2.0, 5.0, 5.25, 7.5, 8.0.
To construct the box plot, we plot these values on a number line. The lower whisker extends from the minimum value (2.0) to Q1 (5.0). The box represents the interquartile range (IQR) and extends from Q1 (5.0) to Q3 (7.5). The median (Q2) is represented by a line in the box. Finally, the upper whisker extends from Q3 (7.5) to the maximum value (8.0).
The resulting box plot should look something like this:
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Sorry, I can't provide a visual representation of the box plot here as it requires spacing and formatting which cannot be done through this text-based format.