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.
9 9 12 12 9 8 8 8 10 8 8 8 11

Explanation:

Step1: Find the Mean

First, sum all the data points. The data is: 9, 9, 12, 12, 9, 8, 8, 8, 10, 8, 8, 8, 11.
Sum = \(8 + 8 + 8 + 8 + 8 + 8 + 9 + 9 + 9 + 10 + 11 + 12 + 12\)
Calculate the sum: \(8\times6 + 9\times3 + 10 + 11 + 12\times2 = 48 + 27 + 10 + 11 + 24 = 120\)
Mean = \(\frac{\text{Sum}}{\text{Number of data points}}=\frac{120}{13}\approx9.23\)

Step2: Find the Median

First, order the data from least to greatest: 8, 8, 8, 8, 8, 8, 9, 9, 9, 10, 11, 12, 12.
There are 13 data points (odd number), so the median is the middle value (the 7th value). The 7th value is 9.

Step3: Find the Mode

The mode is the value that appears most frequently. Count the frequency of each number:

• 8 appears 6 times.
• 9 appears 3 times.
• 10 appears 1 time.
• 11 appears 1 time.
• 12 appears 2 times.

Since 8 appears most frequently, the mode is 8.

Answer:

• Mean: \(\frac{120}{13}\approx9.23\)
• Median: \(9\)
• Mode: \(8\)