In independent random samples of 10 men and 10 women in a coed basketball league, the numbers of points scored per season are given by the back-to-back stemplot below: Row 1 contents are Men; bar; blank; bar; Women. Row 2 contents are 2; bar; 0; bar; 3. Row 3 contents are 8, 5, 4; bar; 1; bar; 4, 7. Row 4 contents are 8, 3, 1; bar; 2; bar; 2, 3, 6, 7. Row 5 contents are 9, 4; bar; 3; bar; 0, 5. Row 6 contents are 6; bar; 4; bar; 1. Part A: Describe the shape of each data set. (3 points) Part B: Michaela analyzed the data and stated that the better measure of center for the women is the mean. Is Michaela correct? Explain your reasoning. (3 points) Part C: Michaela decided there are no outliers in the women's data set. Is she correct? Justify your answer mathematically. (4 points) (10 points)

As you can see in the box plot, the median and mean of the points scored by the women are almost the same. Using the data I've calculated both values:

Me= 24.50

X[bar]= 23.80

The median divides the sample in halves (50-50), it shows you where the middle of the distribution is.

The average shows you the value that centers the distribution, meaning, it is the value around which you'll find most of the data set.

As you can see in the box plots, there are no outliers in both distributions. An outlier is an observation that is significantly distant from the rest of the data set.

Considering the 1st quartile (Q₁), the 3rd quartile (Q₃) and the interquartile range IQR, any value X is considered an outlier if:

X < Q₁ - 1.5 IQR

X > Q₃ + 1.5 IQR

Or extreme outliers if:

X < Q₁ - 3 IQR

X > Q₃ + 3 IQR

For the women data set:

Q₁= 17; Q₃= 30; IQR= 30 - 17= 13

Lower outliers: X < Q₁ - 1.5 IQR= 17-1.5 × 13= -2.5 ⇒ The minimum value recorded is 03, so there are no outliers.

Upper outliers: X > Q₃ + 3 IQR= 30 + 1.5*13= 49.5 ⇒ The maximum value registered is 41, so there are no outliers.

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