The ages of students in a small primary school were recorded in the table below. Age 5 - 6 7 - 8 9 -10 Frequency 29 40 38 Estimate the mean

To estimate the mean of the ages of students in a small primary school, we need to calculate the average age. The formula to calculate the mean is the sum of all the values divided by the total number of values.
In this case, we have three age groups: 5-6, 7-8, and 9-10, with frequencies of 29, 40, and 38 respectively.
To calculate the estimate of the mean, we need to find the midpoint of each age group. The midpoint is the average of the lower and upper limits of each group.
For the age group 5-6, the midpoint is (5 + 6) / 2 = 5.5 For the age group 7-8, the midpoint is (7 + 8) / 2 = 7.5 For the age group 9-10, the midpoint is (9 + 10) / 2 = 9.5
Now, we multiply each midpoint by its respective frequency and add them together.
(5.5 * 29) + (7.5 * 40) + (9.5 * 38) = 159.5 + 300 + 361 = 820.5
Finally, we divide the sum of the products by the total frequency.
820.5 / (29 + 40 + 38) = 820.5 / 107 = 7.6635514
Rounded to two decimal places, the estimate of the mean age is 7.66.
Therefore, the option that is closest to the estimate of the mean is 7.7.