Graphical Analysis In Exercises 19–22, use th...

Question

Graphical Analysis In Exercises 19–22, use the box-and-whisker plot to determine whether the shape of the distribution represented is symmetric, skewed left, skewed right, or none of these. Justify your answer.

Box-and-whisker plot showing data distribution with a range from 20 to 90, highlighting median and quartiles.

Accepted Answer

Hello everyone. Let's take a look at this question together. The box and whisker plot below displays the scores of students on a recent math test. What is the shape of the distribution represented by the plot? And here we have our box and whisker plot, and we want to know is the shape of the distribution answer choice A symmetric, answer choice B positively skewed, answer choice C negatively skewed, or answer choice D, none of these. So, in order to solve this question, we have to recall what we have learned about box and whisker plots to determine what is the shape of the distribution represented by this box and whisker plot that displays the scores of students on a recent math test. And so here we have our box and whisker plot of the recent scores on a math test, and we have to make our whisker length calculations, or our approximations for those calculations, starting with the left whisker, which is the minimum point to our first quartile, and looking at the box and whisker plot, we can identify that our left whisker is approximately 20. And then we can determine the right whisker, which is the 3rd quartile to the maximum point, and using the information in the box and whisker plot, we can identify that the right whisker is approximately 45, and then we can determine the box length, which is the first quartile to the 3rd quartile, which gives a value of approximately 25, and then we determine the median position in the box which from quartile 1 to the median we know is 40 minus 30, giving us a value of 10, and then from the median to the third quartile is 55 minus 40, giving us a value of 15. Therefore, we know the median is slightly closer to the first quartile than the 3rd quartile. And using this information, we can determine the shape of the distribution by analyzing the symmetry and the spread of the plot, where we know that the right tail is significantly longer, as it is 45 versus 20, and the median is not centered as it's closer to the lower quartile. So this indicates more lower scores are clustered near the first quartile, and fewer high scores are stretching the upper end. And based on this information, we know these observations indicate that the distribution is skewed to the right or it is positively skewed. Which, when compared with other distribution types, we can identify that our box and whisker plot data matches a positively skewed distribution type, which has a longer right whisker and a median closer to quartile one. Therefore, the shape of the distribution represented by this plot is answer choice B positively skewed. And all other distribution shapes are incorrect. I hope you found this video to be helpful. Thank you and goodbye.

Graphical Analysis In Exercises 19–22, use the box-and-whisker plot to determine whether the shape of the distribution represented is symmetric, skewed left, skewed right, or none of these. Justify your answer.

Key Concepts

Box-and-Whisker Plot

Distribution Shape

Median and Quartiles

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