In which class interval does the mean lie?

In which class interval does the mean lie?

• A. 5-9
• B. 10-14
• C. 15-19
• D. 20-24

Answer: (C)

The mean is the balancing point of the data. When data are grouped into class intervals, we estimate the mean by weighting each class’s midpoint by its frequency and then dividing by the total frequency: x̄ ≈ Σ(f_i · m_i) / Σ f_i. This estimate will always fall within the overall range of the data, and it tends to land in the interval where the data are most concentrated. If the data are centered around the 15–19 interval, with fewer observations in the outer intervals, the weighted average will lie there. That’s why the mean is in the 15–19 interval. The other intervals would pull the mean toward their ends only if there were more data there, which isn’t indicated by a central concentration.

The mean is the balancing point of the data. When data are grouped into class intervals, we estimate the mean by weighting each class’s midpoint by its frequency and then dividing by the total frequency: x̄ ≈ Σ(f_i · m_i) / Σ f_i. This estimate will always fall within the overall range of the data, and it tends to land in the interval where the data are most concentrated.

If the data are centered around the 15–19 interval, with fewer observations in the outer intervals, the weighted average will lie there. That’s why the mean is in the 15–19 interval. The other intervals would pull the mean toward their ends only if there were more data there, which isn’t indicated by a central concentration.