Which box-and-whisker plot shows the high temperatures in Philadelphia, Pennsylvania, during the first two weeks of March:
39, 41, 33, 57, 34, 30, 47, 33, 49, 52, 32, 53, 37, 43
A. A box-and-whisker plot is shown above a number line that extends from 30 to 58 with 1 unit markings. The box extends from 33 to 49 with a division at 39. There is also a point marked at 39. The whisker on the left extends from 30 to 33. The whisker on the right extends from 49 to 57.
B. A box-and-whisker plot is shown above a number line that extends from 30 to 58 with 1 unit markings. The box extends from 33 to between 50 and 51 with a division at 41. There is also a point marked at 41. The whisker on the left extends from 30 to 33. The whisker on the right extends from between 50 and 51 to 57.
C. A box-and-whisker plot is shown above a number line that extends from 30 to 58 with 1 unit markings. The box extends from 33 to 49 with a division at 40. There is also a point marked at 40. The whisker on the left extends from 30 to 33. The whisker on the right extends from 49 to 57.
D. A box-and-whisker plot is shown above a number line that extends from 30 to 58 with 1 unit markings. The box extends from 33 to between 50 and 51 with a division at 40. There is also a point marked at 40. The whisker on the left extends from 30 to 33. The whisker on the right extends from between 50 and 51 to 57.
A. The correct box-and-whisker plot for the high temperatures in Philadelphia, Pennsylvania, during the first two weeks of March is:
A box-and-whisker plot is shown above a number line that extends from 30 to 58 with 1 unit markings. The box extends from 33 to 49 with a division at 39. There is also a point marked at 39. The whisker on the left extends from 30 to 33. The whisker on the right extends from 49 to 57.
To determine which box-and-whisker plot represents the high temperatures in Philadelphia during the first two weeks of March, we need to understand how to construct a box-and-whisker plot.
A box-and-whisker plot is a visual representation of a set of numerical data, showing the distribution and variability of the data. It consists of several components: the minimum value (the left-most whisker), the lower quartile (the bottom edge of the box), the median (the line inside the box), the upper quartile (the top edge of the box), and the maximum value (the right-most whisker).
Now, let's analyze each option to see which one matches the given dataset:
Option A: This plot has a whisker on the left extending from 30 to 33, which matches the minimum temperature. The whisker on the right extends from 49 to 57, which matches the maximum temperature. The box extends from 33 to 49 with a division at 39, which suggests the lower quartile, median, and upper quartile respectively. This option could be a potential match.
Option B: This plot has a whisker on the left extending from 30 to 33, which matches the minimum temperature. The whisker on the right extends from between 50 and 51 to 57, which is higher than the maximum temperature. Therefore, this option does not match the given dataset.
Option C: This plot has a whisker on the left extending from 30 to 33, matching the minimum temperature. The whisker on the right extends from 49 to 57, matching the maximum temperature. The box extends from 33 to 49 with a division at 40, which is different from the given data. Therefore, this option does not match the given dataset.
Option D: This plot has a whisker on the left extending from 30 to 33, which matches the minimum temperature. The whisker on the right extends from between 50 and 51 to 57, which is higher than the maximum temperature. The box extends from 33 to between 50 and 51, with a division at 40, which does not match the given dataset. Therefore, this option does not match the given data.
Based on the analysis, Option A is the only box-and-whisker plot that matches the given dataset of high temperatures in Philadelphia during the first two weeks of March.
To create a box-and-whisker plot for the given high temperatures in Philadelphia during the first two weeks of March, let's first order the temperatures in ascending order:
30, 32, 33, 33, 34, 37, 39, 41, 43, 47, 49, 52, 53, 57
The five-number summary (minimum, first quartile, median, third quartile, maximum) can be obtained as follows:
Minimum: 30
First Quartile (Q1): 34
Median (Q2): 41
Third Quartile (Q3): 49
Maximum: 57
Now, let's evaluate the provided options:
A. The box-and-whisker plot extends from 33 to 49, with a division at 39. This does not accurately represent the quartiles and the whiskers on both sides are incorrect.
B. The box-and-whisker plot extends from 33 to between 50 and 51, with a division at 41. This does not accurately represent the quartiles and the whiskers on both sides are incorrect.
C. The box-and-whisker plot extends from 33 to 49, with a division at 40. This accurately represents the quartiles, but the maximum value is incorrect.
D. The box-and-whisker plot extends from 33 to between 50 and 51, with a division at 40. This accurately represents the quartiles and the whiskers, but the minimum value is incorrect.
Based on the evaluation, none of the provided options accurately depict the high temperatures in Philadelphia during the first two weeks of March.