Question

I need help with part A bit if u can help me with every I will give you 5 stars ⭐️

Answer 1

The question provides us with boxplots for the population of males and females that went to the cinema each day for a month.

PART A

Find the Interquartile Range (IQR) for Males:

The IQR is gotten by subtracting Q1 from Q3. (where Q1 and Q3 are the first and third Quartiles of the data).

That is:

`\text{IQR}=Q_3-Q_1`

The Q1 and Q3 values are read from the edge of the box in the boxplot.

This is depicted below:

We need to extend lines from these two edges down the axis below to estimate what the values of Q1 and Q3 could be.

This is done below:

From the above, we can estimate that:

`\begin{gathered} Q_1\approx4\text{ (rough estimate)} \\ Q_3\approx14\text{ (rough estimate)} \end{gathered}`

Thus, we can calculate IQR for males as:

`\begin{gathered} \text{IQR}=Q_3-Q_1 \\ \therefore\text{IQR}\approx14-4 \\ \\ \text{IQR}\approx10 \end{gathered}`

IQR for males is roughly estimated to be 10.

PART B:

Finding the difference between the medians of the distributions for the males and females.

The median is the line where in between Q3 and Q1. That is, the line within the box.

Once again, we shall read the values of the medians for the Male and female distributions off the box plots by tracing

the lines to the bottom axis.

The medians are represented on the above image as Mm for median for males and Mf for median for females.

From observation, we can estimate the values for these medians as:

`\begin{gathered} M_m\approx9 \\ M_f\approx6 \end{gathered}`

Therefore, the difference in medians is:

`\begin{gathered} M_m-M_f\approx9-6 \\ M_m-M_f\approx3 \end{gathered}`

PART C:

The Male distribution is clearly skewed to the right, while the Female distribution is slightly skewed to the right. However, the Female distribution has an outlier as well.

From the properties of Mean, we know that Mean is readily affected by outliers and skewed distributions.

Thus, the best estimator for the measure of center is Median.

PART D:

A possible reason for the outlier in the Female boxplot distribution could be that the movie was showing for the last

time. This made people rush to the cinema and thus, the number of females that went to the cinema on that last day resulted in an outlier in the female distribution.