Question

the letters a, b, and c are marked on the histogram. describe the shape of the data. then determine which is the mean, which is the median, and which is the mode. justify your answers.

which description below best describes the shape of the distribution?

• skewed right
• uniform
• symmetric
• skewed left

in this distribution, how is the mode determined?
a. the mode is the data entry that has the lowest frequency.
b. the mean, median, and mode are all equal.
c. the mode is the data entry that has the highest frequency.
d. the mode cannot be identified.

the mode is labeled a.

in this distribution, how is the mean determined?
a. the mean is to the right of the median and mode.
b. the mean is to the left of the median and mode.
c. the mean cannot be identified.
d. the mean, median, and mode are all equal.

the mean is labeled c.

in this distribution, how is the median determined?
a. the median is to the left of the mean and to the right of the mode.
b. the median cannot be identified.
c. the median is to the right of the mean and to the left of the mode.
d. the mean, median, and mode are all equal.

Explanation:

Identify distribution shape

Using the Histogram Shape Analysis knowledge point

• The histogram has a peak on the left side (around 3 days) and a long tail extending to the right (up to 15 days).
• This asymmetric pattern with a tail pointing towards the larger values indicates a right-skewed distribution.

Determine the mode

Using the Mode of Data knowledge point

• The mode is the value that occurs most frequently, corresponding to the tallest bar in the histogram.
• On the histogram, the tallest bar is at 3 days, which is marked by the leftmost vertical line labeled \(A\).
• Therefore, the mode is determined as the data entry with the highest frequency, labeled \(A\).

Determine the mean

Using the Mean Calculation knowledge point

• In a right-skewed distribution, the mean is pulled toward the long right tail by the larger values.
• Consequently, the mean is the largest of the three measures of central tendency, positioned furthest to the right.
• On the histogram, the rightmost vertical line is labeled \(C\), representing the mean.
• Therefore, the mean is to the right of the median and mode, labeled \(C\).

Determine the median

Using the Median Calculation knowledge point

• In a skewed distribution, the median lies between the mode (the peak) and the mean (pulled toward the tail).
• On the histogram, the middle vertical line is labeled \(B\), representing the median.
• Therefore, the median is to the left of the mean and to the right of the mode, labeled \(B\).

Answer:

Question 1

• Skewed right (Correct answer)
• Uniform
• Symmetric
• Skewed left

Question 2

• A. The mode is the data entry that has the lowest frequency.
• B. The mean, median, and mode are all equal.
• C. The mode is the data entry that has the highest frequency. (Correct answer)
• D. The mode cannot be identified.

Question 3

The mode is labeled <blank>A</blank>

Question 4

• A. The mean is to the right of the median and mode. (Correct answer)
• B. The mean is to the left of the median and mode.
• C. The mean cannot be identified.
• D. The mean, median, and mode are all equal.

Question 5

The mean is labeled <blank>C</blank>

Question 6

• A. The median is to the left of the mean and to the right of the mode. (Correct answer)
• B. The median cannot be identified.
• C. The median is to the right of the mean and to the left of the mode.
• D. The mean, median, and mode are all equal.

Question 7

The median is labeled <blank>B</blank>