Question

the following data represent the amount of time (in minutes) a random sample of eight students took to complete the online portion of an exam in a particular statistics course. compute the mean, median, and mode time. 68.3, 76.7, 92.4, 111.7, 128.4, 93.6, 94.7, 116.1 compute the mean exam time. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the mean exam time is 97.74 (round to two decimal places as needed.) b. the mean does not exist. compute the median exam time. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the median exam time is 94.15 (round to two decimal places as needed.) b. the median does not exist. compute the mode exam time. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the mode is (round to two decimal places as needed. use a comma to separate answers as needed.) b. the mode does not exist.

Explanation:

Mean Calculation (already provided as 97.74, but let's verify):

Step1: Sum the data values

The data points are \( 68.3, 76.7, 92.4, 111.7, 128.4, 93.6, 94.7, 116.1 \).
Summing them: \( 68.3 + 76.7 + 92.4 + 111.7 + 128.4 + 93.6 + 94.7 + 116.1 \)
\( = (68.3 + 76.7) + (92.4 + 111.7) + (128.4 + 93.6) + (94.7 + 116.1) \)
\( = 145 + 204.1 + 222 + 210.8 \)
\( = 145 + 204.1 = 349.1 \); \( 349.1 + 222 = 571.1 \); \( 571.1 + 210.8 = 781.9 \)

Step2: Divide by the number of data points (n = 8)

Mean \( = \frac{781.9}{8} = 97.7375 \approx 97.74 \) (rounded to two decimals).

Median Calculation (already provided as 94.15, let's verify):

Step1: Order the data

Ordered data: \( 68.3, 76.7, 92.4, 93.6, 94.7, 111.7, 116.1, 128.4 \)

Step2: Find the middle (n = 8, even, so average of 4th and 5th terms)

4th term: \( 93.6 \); 5th term: \( 94.7 \)
Median \( = \frac{93.6 + 94.7}{2} = \frac{188.3}{2} = 94.15 \)

Mode Calculation:

Step1: Check frequency of each value

All values appear once (no repeated values).

for Mode:
The mode is the most frequently occurring value. In this dataset, each time value (68.3, 76.7, 92.4, 111.7, 128.4, 93.6, 94.7, 116.1) appears exactly once. Since no value is repeated, there is no mode.

Answer:

(Mode):
B. The mode does not exist.

Final Answers (Summary):

• Mean: 97.74 (Option A)
• Median: 94.15 (Option A)
• Mode: B. The mode does not exist.