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 100 to 600, highlighting median and quartiles.

Accepted Answer

Hello everyone. Let's take a look at this question together. The box and whisker plot below shows the weights of apples in a harvest in grams. What is the shape of the distribution represented by the plot? And here we have our box and whisker plot, which we have to determine is the shape of the distribution answer choice A negatively skewed. Answer choice B positively skewed, answer choice C symmetric, 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 plot of the weights of apples in a harvest in grams. And so looking at our box and whisker plot. We know that to determine the shape of the distribution, we have to calculate the whisker lengths, starting with the left whisker, which is the minimum 2 quartile 1, and based on our box and whisker plot, we can identify that the length of the left whisker is approximately 25 g, and then we can calculate the right whisker, which is the third quartile, to the maximum point. Which the length of the right whisker is approximately 55 g, and using the lengths of the whiskers, we can determine the shape of the distribution and starting off with answer choice A, which says negatively skewed, we know that in the image the left whisker is shorter. And the median is not closer to the 3rd quartile, as well as the tail is on the right and not the left, therefore, it cannot be negatively skewed. Then answer choice B, which says positively skewed. We know that the right tail is longer than the left tail, indicating a clear asymmetry with a longer right tail, as well as the right whisker is more than the left whisker, and the median is not centered in the box, as it is closer to the first quartile. Therefore, these features clearly indicate a positively skewed distribution. Therefore, we know the shape of the distribution of our box and whisker. The plot is positively skewed. As we know, it cannot be negatively skewed, as well as symmetric, since the right whisker is much longer than the left whisker, and the median is closer to quartile one and not centered, so the distribution is unbalanced, telling us it is not symmetric, which makes answer choice B positively skewed, the correct answer, and all other answer choices are incorrect. I hope you found this video to be helpful. Thank you and goodbye.