Questions: HW Score: 89.39%, 9.83 of 11 points Points: 0 of 1 Class Relative Frequency 30-39 0.025 40-49 0.025 50-59 0.075 60-69 0.10 70-79 0.325 80-89 0.25 90-99 0.2 (b) Draw a relative frequency histogram of the data. Choose the correct answer below. A. Homework Scores (c) Determine the mean and median score. The mean score is and the median score is (Type integers or decimals. Do not round.)

HW Score: 89.39%, 9.83 of 11 points
Points: 0 of 1
Class Relative Frequency
30-39 0.025
40-49 0.025
50-59 0.075
60-69 0.10
70-79 0.325
80-89 0.25
90-99 0.2
(b) Draw a relative frequency histogram of the data. Choose the correct answer below.
A. Homework Scores
(c) Determine the mean and median score.

The mean score is and the median score is (Type integers or decimals. Do not round.)

Transcript text: HW Score: 89.39\%, 9.83 of 11 points Points: 0 of 1 \begin{tabular}{cc} Class & \begin{tabular}{c} Relative \\ Frequency \end{tabular} \\ \hline $30-39$ & 0.025 \\ \hline $40-49$ & 0.025 \\ \hline $50-59$ & 0.075 \\ \hline $60-69$ & 0.10 \\ \hline $70-79$ & 0.325 \\ \hline $80-89$ & 0.25 \\ \hline $90-99$ & 0.2 \\ \hline \end{tabular} (b) Draw a relative frequency histogram of the data. Choose the correct answer below. A. Homework Scores (c) Determine the mean and median score. The mean score is $\square$ and the median score is $\square$ (Type integers or decimals. Do not round.)

Solution

Solution Steps

Step 1: Identify the correct histogram

To draw a relative frequency histogram, we need to match the given relative frequencies with the correct histogram. The given relative frequencies are:

40-49: 0.025
50-59: 0.075
60-69: 0.175
70-79: 0.325
80-89: 0.25
90-99: 0.15

By comparing these values with the histograms provided, we can see that the first histogram matches these relative frequencies.

Step 2: Calculate the mean score

To calculate the mean score, we use the midpoints of each class and multiply them by their relative frequencies, then sum these products.

Midpoints:

40-49: 44.5
50-59: 54.5
60-69: 64.5
70-79: 74.5
80-89: 84.5
90-99: 94.5

Mean score calculation: \[ \text{Mean} = (44.5 \times 0.025) + (54.5 \times 0.075) + (64.5 \times 0.175) + (74.5 \times 0.325) + (84.5 \times 0.25) + (94.5 \times 0.15) \] \[ \text{Mean} = 1.1125 + 4.0875 + 11.2875 + 24.2125 + 21.125 + 14.175 \] \[ \text{Mean} = 75 \]

Step 3: Calculate the median score

To find the median score, we need to determine the cumulative relative frequencies and find the class where the cumulative relative frequency reaches 0.5.

Cumulative relative frequencies:

40-49: 0.025
50-59: 0.1 (0.025 + 0.075)
60-69: 0.275 (0.1 + 0.175)
70-79: 0.6 (0.275 + 0.325)
80-89: 0.85 (0.6 + 0.25)
90-99: 1 (0.85 + 0.15)

The median falls in the 70-79 class because the cumulative relative frequency reaches 0.5 in this class. The exact median can be interpolated within this class.