Final answer:
To approximate the mean of the given grouped data, find the midpoint for each class interval, multiply each by its corresponding frequency, sum these products, and then divide by the total frequency. Round the final value to the nearest whole number to obtain the approximate mean.
Step-by-step explanation:
To approximate the mean of the given grouped data, we calculate the midpoint for each group, then multiply the midpoint by the frequency for that group. Next, we sum those products and divide by the total frequency.
- For the 8-11 group, the midpoint is (8+11)/2 = 9.5. The product is 9.5 * 49.
- For the 12-15 group, the midpoint is (12+15)/2 = 13.5. The product is 13.5 * 27.
- For the 16-19 group, the midpoint is (16+19)/2 = 17.5. The product is 17.5 * 37.
- For the 20-23 group, the midpoint is (20+23)/2 = 21.5. The product is 21.5 * 10.
- For the 24-27 group, the midpoint is (24+27)/2 = 25.5. The product is 25.5 * 24.
Adding the products, we get the sum of the weighted midpoints. To find the mean, divide this sum by the total frequency:
- Total frequency = 49 + 27 + 37 + 10 + 24
- Sum of weighted midpoints = (9.5 * 49) + (13.5 * 27) + (17.5 * 37) + (21.5 * 10) + (25.5 * 24)
- Calculate the mean and round to the nearest whole number.
Substitute the values and perform the calculations to find the mean. Rounding to the nearest whole number provides the approximate mean of the grouped data.