Answer :
Based on this analysis, we can conclude that any of the data sets (1, 3, or 4) could be used for the box-and-whisker plot shown, depending on the specific context and purpose of the plot.
To determine which set of data could be used for the given box-and-whisker plot, we need to first understand what a box-and-whisker plot represents.
A box-and-whisker plot is a graphical representation of a set of data that shows the median, quartiles, and range of the data. The median is the middle value when the data is arranged in order from smallest to largest. The quartiles divide the data into four equal parts, with the first quartile (Q₁) being the value at the 25th percentile, the second quartile (Q₂) being the median, and the third quartile (Q₃) being the value at the 75th percentile. The range is the difference between the largest and smallest values in the data set.
Now, looking at the given data sets, we can calculate the median, quartiles, and range for each set to determine which one could be used for the box-and-whisker plot shown.
- Set 1: 67, 74, 78, 69, 78, 70, 67, 72, 69
Median = 70
Q₁ = 67
Q₃ = 74
Range = 11 (78 - 67)
- Set 2: 67, 74, 78, 69, 80, 70, 67, 72, 69
Median = 70
Q₁ = 67
Q₃ = 74
Range = 13 (80 - 67)
- Set 3: 67, 74, 78, 69, 78, 71, 67, 72, 69
Median = 71
Q₁ = 67
Q₃ = 74
Range = 11 (78 - 67)
- Set 4: 68, 74, 78, 69, 78, 70, 68, 72, 69
Median = 69
Q₁ = 68
Q₃ = 74
Range = 10 (78 - 68)
From these calculations, we can see that sets 1, 3, and 4 all have the same quartile values and similar ranges. However, the median for set 3 is slightly higher than the others, which could affect the appearance of the box-and-whisker plot. Set 2 has a higher range due to the outlier value of 80, which could also affect the appearance of the plot.
Based on this analysis, we can conclude that any of the data sets (1, 3, or 4) could be used for the box-and-whisker plot shown, depending on the specific context and purpose of the plot. However, set 2 may not be the best choice due to the outlier value.
To know more about data sets, refer
https://brainly.com/question/28168026
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