Using the midpoints to approximate the mean for this grouped distribution, which value best approximates the mean?

Using the midpoints to approximate the mean for this grouped distribution, which value best approximates the mean?

• A. 11.5
• B. 15.9
• C. 18.0
• D. 20.0

Answer: (B)

When estimating a mean for grouped data, you treat each class by its midpoint and weight that midpoint by how many observations fall in that class. The mean is then the weighted average of those midpoints: sum of (midpoint × frequency) divided by the total frequency. This gives you the value that best represents the center of the distribution based on where most data lie. In this distribution, the data are centered in the midrange, so the weighted average of the class midpoints lands near 15.9. That value best reflects the overall balance point of the data. The other options lie farther from where most observations occur, so they don’t represent the center as well.

When estimating a mean for grouped data, you treat each class by its midpoint and weight that midpoint by how many observations fall in that class. The mean is then the weighted average of those midpoints: sum of (midpoint × frequency) divided by the total frequency. This gives you the value that best represents the center of the distribution based on where most data lie.

In this distribution, the data are centered in the midrange, so the weighted average of the class midpoints lands near 15.9. That value best reflects the overall balance point of the data. The other options lie farther from where most observations occur, so they don’t represent the center as well.