Calculate the mean for grouped data.

Calculate the mean for grouped data.

• A. Sum of frequency multiplied by height / total frequency
• B. Sum of data values divided by number of data points
• C. The median of the group midpoints
• D. The mode of the grouped data

Answer: (A)

When data are grouped, the mean is estimated by using the class midpoints as the representative values for each group. For every class, multiply its midpoint by the frequency in that class, then add these products up and divide by the total number of observations. In formula form: mean ≈ Σ(f_i × m_i) / N, where f_i is the frequency of a class, m_i is its midpoint, and N is the total frequency. This approach works because you don’t know the exact values within each class, so the midpoint is the best single value to stand in for all observations in that class. Using the raw data values divided by the number of data points would give the exact mean only if you had all individual data points. Taking the median of the midpoints would not yield the average, and identifying the mode would reflect the most common class rather than the average.

When data are grouped, the mean is estimated by using the class midpoints as the representative values for each group. For every class, multiply its midpoint by the frequency in that class, then add these products up and divide by the total number of observations. In formula form: mean ≈ Σ(f_i × m_i) / N, where f_i is the frequency of a class, m_i is its midpoint, and N is the total frequency. This approach works because you don’t know the exact values within each class, so the midpoint is the best single value to stand in for all observations in that class. Using the raw data values divided by the number of data points would give the exact mean only if you had all individual data points. Taking the median of the midpoints would not yield the average, and identifying the mode would reflect the most common class rather than the average.