Question

the number of credits being taken by a sample of 13 full-time college students are listed below. find the mean, median, and mode of the data, if possible. if any measure cannot be found or does not represent the center of the data, explain why.

5 7 8 8 5 4 4 4 6 4 4 4 5

d. the median does not represent the center because it is not a data value.
e. the data set does not have a median.

find the mode. select the correct choice below and, if necessary, fill in the answer box to complete your choice.

a. the mode(s) is/are 4.
(type an integer or decimal rounded to one decimal place as needed. use a comma to separate answers as needed.)
b. the data set does not have a mode.

does (do) the mode(s) represent the center of the data?

a. the mode(s) represent(s) the center.
b. the mode(s) does (do) not represent the center because it (they) is (are) not a data value.
c. the data set does not have a mode.
d. the mode(s) does (do) not represent the center because it (one) is the largest data value.
e. the mode(s) does (do) not represent the center because it (one) is the smallest data value.

Explanation:

Find the mode of the dataset

$$ \text{Data: } 5, 7, 8, 8, 5, 4, 4, 4, 6, 4, 4, 4, 5 $$

$$ \text{Frequencies: } 4 ightarrow 6 \text{ times},\ 5 ightarrow 3 \text{ times},\ 6 ightarrow 1 \text{ time},\ 7 ightarrow 1 \text{ time},\ 8 ightarrow 2 \text{ times} $$

$$ \text{Mode} = 4 $$

Determine if the mode represents the center

$$ \text{Sorted Data: } 4, 4, 4, 4, 4, 4, 5, 5, 5, 6, 7, 8, 8 $$

$$ \text{Minimum value} = 4 $$

$$ \text{The mode (4) is the smallest data value, so it does not represent the center.} $$

Answer:

Question 1

• A. The mode(s) is/are 4 (Correct answer)
• B. The data set does not have a mode.

Question 2

• A. The mode(s) represent(s) the center.
• B. The mode(s) does (do) not represent the center because it (they) is (are) not a data value.
• C. The data set does not have a mode.
• D. The mode(s) does (do) not represent the center because it (one) is the largest data value.
• E. The mode(s) does (do) not represent the center because it (one) is the smallest data value. (Correct answer)