A data set has values 2 (8 times), 5 (12 times), and 7 (4 times). What is the mean?

A data set has values 2 (8 times), 5 (12 times), and 7 (4 times). What is the mean?

• A. 3.5
• B. 4.33
• C. 5.0
• D. 4.0

Answer: (B)

Mean is the average value, found by adding up all data points and dividing by how many data points there are. When a value appears several times, treat each appearance as a separate data point and weight accordingly. Here, multiply each value by its frequency and add: 2 appears 8 times contributes 2 × 8 = 16 5 appears 12 times contributes 5 × 12 = 60 7 appears 4 times contributes 7 × 4 = 28 Sum of all values = 16 + 60 + 28 = 104. Total number of observations = 8 + 12 + 4 = 24. So the mean is 104 divided by 24, which equals 104/24 = 4.333..., or about 4.33. This result reflects the frequencies in the data, giving more weight to the value 5 because it appears most often. The other numbers would not match this weighted average, since they don’t account for how often each value occurs.

Mean is the average value, found by adding up all data points and dividing by how many data points there are. When a value appears several times, treat each appearance as a separate data point and weight accordingly.

Here, multiply each value by its frequency and add:

2 appears 8 times contributes 2 × 8 = 16

5 appears 12 times contributes 5 × 12 = 60

7 appears 4 times contributes 7 × 4 = 28

Sum of all values = 16 + 60 + 28 = 104. Total number of observations = 8 + 12 + 4 = 24. So the mean is 104 divided by 24, which equals 104/24 = 4.333..., or about 4.33.

This result reflects the frequencies in the data, giving more weight to the value 5 because it appears most often. The other numbers would not match this weighted average, since they don’t account for how often each value occurs.