What box-and-whisker plot represents the following monthly sales, in millions of dollars, of audio devices: 15 4 9 16 10 16 8 14 25 34?
To create a box-and-whisker plot, we first need to order the data from least to greatest:
4, 8, 9, 10, 14, 15, 16, 16, 25, 34
The plot will have five components: minimum, lower quartile (Q1), median (Q2), upper quartile (Q3), and maximum.
Minimum: The smallest value in the dataset is 4.
Maximum: The largest value in the dataset is 34.
Median (Q2): To find the median, we take the average of the two middle numbers. In this case, the two middle numbers are 14 and 15. Therefore, the median is (14 + 15)/2 = 14.5.
Lower Quartile (Q1): To find Q1, we determine the median of the lower half of the data. The lower half of the data includes 4, 8, 9, and 10. Therefore, the median of the lower half is (8 + 9)/2 = 8.5.
Upper Quartile (Q3): To find Q3, we determine the median of the upper half of the data. The upper half of the data includes 16, 16, 25, and 34. Therefore, the median of the upper half is (16 + 25)/2 = 20.5.
Now, we can draw the box-and-whisker plot using the minimum, Q1, median (Q2), Q3, and maximum values:
Minimum: 4
Q1: 8.5
Median (Q2): 14.5
Q3: 20.5
Maximum: 34
The box will be formed by the lines connecting Q1 and Q3 (with a line inside the box representing the median). The whiskers will extend from the box to the minimum and maximum values.
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