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.

Explanation:

Identify the distribution shape

Using the Histogram Shape Analysis knowledge point
The histogram has a long tail extending to the right, with the highest frequencies concentrated on the left side. This indicates that the distribution is skewed right.

Determine the mode

Using the Measures of Central Tendency knowledge point
The mode is the data value with the highest frequency, corresponding to the tallest bar on the histogram. Therefore, the mode is labeled A, which aligns with the peak of the distribution.

Determine the mean

Using the Measures of Central Tendency knowledge point
In a right-skewed distribution, the mean is pulled toward the long right tail by extremely large values. Consequently, the mean is located to the right of both the median and the mode, which corresponds to label C.

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

• 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.