a. mean: To find the mean, sum up all the ages and divide by the number of teachers:
27 + 52 + 38 + 57 + 27 + 52 + 27 + 48 + 48 + 43 = 419
There are 10 teachers, so the mean age is 419/10 = 41.9.
b. median: To find the median, organize the ages in ascending order:
27, 27, 27, 38, 43, 48, 48, 52, 52, 57
Since there are an even number of teachers, we take the average of the middle two values: (43 + 48)/2 = 45.5.
c. mode: The mode is the value that appears the most number of times. In this case, the mode is 27 because it appears 3 times, which is more than any other value.
d. midrange: The midrange is the average of the maximum and minimum values. The maximum value is 57 and the minimum value is 27, so the midrange is (57 + 27)/2 = 42.
Therefore, the correct answers are:
a. mean: 41.9
b. median: 45.5
c. mode: 27
d. midrange: 42