Question

N 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)

Answer 1

Answer:

Step-by-step explanation:

Hello!

a)

To compare both datasets I've made a box plot for them.

The yellow one belongs to the points scored by the men and the green one is for the points scored by the women.

Women: The box seems symmetrical, the median and the mean (black square) are almost the same. The whiskers are almost the same length, you could say that in general the points scored by the women have a symmetrical distribution.

Men: The box looks a little skewed to the right, the median is closer to the 1st quantile and the mean is greater than the median. The whiskers are the same length, in general the distribution seems almost symmetrical.

b)

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. It summarizes best the sample information and therefore is a better measure of center.

c.

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. They usually represent experimental errors (such as a measurement) or atypical observations. Some statistical measurements, such as the sample mean, are severely affected by this type of values and their presence tends to cause misleading results on a statistical analysis.

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.

I hope this helps!