Question

prob & stats ch 5b day 7 - skewed data
name:____ hr:____

1. draw in the lines and label the mean and median for each of the following scenarios:
2. match the proper shape of a distribution to the median and mean scenarios below.

a) mean is significantly higher than the median 1. roughly symmetric
b) mean is significantly lower than the median 2. skewed right
c) mean and median are about the same. 3. skewed left

1. the median of a certain distribution is 23 and the mean is 30. based on this information, which of the following is a possible description of the distribution’s shape?

(a) roughly symmetric (b) skewed right (c) skewed left.

1. mr. downing graded his favorite five kids’ tests and the scores were: 86, 90, 92, 97, 100. then, he graded one more test that had a score of 42. what shape will the distribution of these test scores take (symmetric, skewed right, or skewed left)?

based on your answer, should downing use mean or median to report the center of the data?

Explanation:

Step1: Recall distribution - shape rules

In a skewed - right distribution, the mean is pulled in the direction of the long right - tail and is greater than the median. In a skewed - left distribution, the mean is pulled in the direction of the long left - tail and is less than the median. In a roughly symmetric distribution, the mean and median are approximately equal.

Step2: Answer question 2

a) When the mean is significantly higher than the median, the distribution is skewed right. So a) matches 2.
b) When the mean is significantly lower than the median, the distribution is skewed left. So b) matches 3.
c) When the mean and median are about the same, the distribution is roughly symmetric. So c) matches 1.

Step3: Answer question 3

Given that the median is 23 and the mean is 30 (mean > median), the distribution is skewed right.

Step4: Answer question 4

The original scores are 86, 90, 92, 97, 100. When a score of 42 is added, this low out - lier will pull the mean down. The distribution will be skewed left. Since the distribution is skewed left, the median is a better measure of the center as the mean is affected by the out - lier.

Answer:

2.
a) 2. Skewed Right
b) 3. Skewed Left
c) 1. Roughly Symmetric

1. (b) Skewed right
2. Skewed Left; Median