To find the value that best represents all the measures of center for this data set, we need to calculate the mean, median, and mode:
Mean:
To find the mean, we add up all the numbers and divide by the total count:
(48 + 12 + 11 + 45 + 48 + 48 + 43 + 32) / 8 = 37.5
Median:
To find the median, we first need to arrange the numbers from smallest to largest:
11, 12, 32, 43, 45, 48, 48, 48
There are 8 values in this data set, so the median is the middle value. In this case, the middle value is 45, so:
Median = 45
Mode:
To find the mode(s), we look for the value(s) that appear most frequently in the data set. In this case, the number 48 appears three times, which is more than any other number:
Modes = 48
Since the mean, median, and mode are all different values in this data set, there is no one value that best represents all three measures of center.