For the given data set, find the
a. mean
b. median
c. mode (or state that there is no mode)
and
d. midrange.
The ages of the teachers in the mathematics departmetn of a certain high school are shown below.
27, 52, 38, 57, 27, 52, 27, 48, 48, 43
a. 26.5
b. 45.5
c. 27
d. 42
a. 41.9
b. 45.5
c. 27
d. 42
a. 31.3
b. 45.5
c. 27
d. 42
a. 41.9
b. 45.5
c. 48
d. 42
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