Question

Use the box plots comparing the number of males and number of females attending the latest superhero movie each day for a month to answer the questions.
Two box plots shown. The top one is labeled Males. Minimum at 1, Q1 at 3, median at 10.5, Q3 at 14, maximum at 21, and a point at 30. The bottom box plot is labeled Females. Minimum at 0, Q1 at 15, median at 18, Q3 at 21, no maximum shown

Part A: Estimate the IQR for the males' data. (2 points)

Part B: Estimate the difference between the median values of each data set. (2 points)

Part C: Describe the distribution of the data and if the mean or median would be a better measure of center for each. (4 points)

Part D: Provide a possible reason for the outlier in the data set. (2 points)

Answer 1

Answer:

(A) The IQR for the males' data is 11.

(B) The difference between the median values of each data set = 18 - 10.5 = 7.5.

(C) The distribution of the males' data is an asymmetrical distribution or we can say the right-skewed distribution and the median would be a better measure of the center.

The distribution of the females' data is a symmetrical distribution or we can say the normal distribution and the mean would be a better measure of the center.

(D) In the males' data, we see that there is only one outlier at a value of 30.

Step-by-step explanation:

We are given the following information about the two box plots of male and female below;

The top one is labeled Males: Minimum at 1, Q1 at 3, median at 10.5, Q3 at 14, maximum at 21, and a point at 30.

The bottom box plot is labeled as Females: Minimum at 0, Q1 at 15, median at 18, Q3 at 21, no maximum is shown.

(A) The Interquartile range (IQR) is the difference between the third quartile and the first quartile of the data set.

In a box plot representing the males;

$Q_3$ = 14 and $Q_1$ = 3

So, IQR = $Q_3$ - $Q_1$ = 14 - 3 = 11.

Hence, the IQR for the males' data is 11.

(B) The median value of the males' data is given as 10.5 and the median value of the females' data is given as 18.

So, the difference between the median values of each data set = 18 - 10.5 = 7.5.

(C) The distribution of the males' data is an asymmetrical distribution or we can say the right-skewed distribution because the values after the third quartile are very far and also the lower quartile range is much larger than the upper quartile range. Also, there is one outlier in males' data also.

So, for any asymmetrical distribution, the median would be a better measure of the center as it does not take into account the outliers' value and gives the middlemost data value.

The distribution of the females' data is a symmetrical distribution or we can say the normal distribution because the data values are equally spread and the median is at the center of the two quartile values.

So, for any symmetrical distribution, although the mean and median are the same; the mean would be a better measure of the center as it does take into account all the data values and gives the average of the data set.

(D) Yes, there is one outlier in the males' data set. Outliers are those values that fall very far from all other values.

In a box plot data, outliers are represented as single points outside the whiskers.

In the males' data, we see that there is only one outlier at a value of 30. This represents a case in which a male attended the movie theater on the 30th day of the month. This is an invalid case since the maximum of the male plot is at 21, which means that no males attended the movie after the 21st.

Answer 2

Answer:

yessir

Step-by-step explanation:

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