1. Below is the histogram for the number of medals won for the n = 203 countries

Question

1. Below is the histogram for the number of medals won for the n = 203 countries that participated in
the 2008 Summer Olympics in Beijing, along with the detailed summary statistics for this variable:

a. Is this distribution symmetric, left-skewed, or right-skewed? How do you know?

b. The mean for these data is 4.70. Give a reasonable guess of the median for these data.

c. Based on the rule we used in class and in your text, are there any potential low or high outliers in the
dataset? Show your work.

Explanation / Answer

a. This is a right skewed distsribution also called positive skewed distribution because the distribution has a shorter left tail and a longer right tail. Tail is measured from the mean towards the left and right. Here, the mean is 4.7 and so left tail is shorter.

b. For a right skewed distribution, the median will be less than the mean which is 4.7 Also, median will be closer to the first quartile (25th percentile) value which is 0. Here we can clearly see the frequency of ZERO value is 150 and so that should be the median.

c. If the mean is 4.70 and median 0, then the maximum value of 110 is definitely an outlier. We can usually tell a outlier with this formula - Anything below Q1 minus 1.5 times the IQR or above Q3 plus 1.5 times the IQR will be an outlier usually.

IQR here is the Inter Quartile Range which is Q3 - Q1 or the difference between the 75th quartile and 25th quartile values.

Here, IQR = Q3 - Q1 = 3 - 0 = 3

Range for outliers = 3 + 1.5*3 and 0 - 1.5*3 = > 7.5 and < -4.5

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