Find the mean of the data set: 23, 32, 38, 19, 28, 27, 18, 36, 29, 26, 32
The mean is the sum of all the numbers divided by the total count of the numbers.
To get the sum, add all the numbers together:
23 + 32 + 38 + 19 + 28 + 27 + 18 + 36 + 29 + 26 + 32 = 308
To get the count, count the number of items in the set:
11
Now divide the sum by the count to get the mean:
308 / 11 = 28
Therefore, the mean of the data set is 28.
Find the median of the data set: 56, 60, 60, 40, 60, 75, 40, 25, 53, 34, 62, 76
To find the median of a data set, we need to arrange the numbers in order from smallest to largest.
25, 34, 40, 40, 53, 56, 60, 60, 60, 62, 75, 76
The median is the middle value. If there are an odd number of values, the median is the middle number. If there are an even number of values, the median is the average of the two middle numbers.
In this case, there are 12 values, so we have an even number of values. The two middle numbers are 56 and 60. To find the median, we take the average of these two numbers:
(56 + 60) / 2 = 58
Therefore, the median of the data set is 58.
Find the mean, median, and modes of the data set: 91, 93, 89, 97, 89, 98, 94, 93.
To find the mean of a set of numbers, we add up all the numbers in the set and divide by the total count of numbers.
Mean:
(91 + 93 + 89 + 97 + 89 + 98 + 94 + 93) / 8 = 92
The mean of the data set is 92.
To find the median, we first need to arrange the numbers from smallest to largest:
89, 89, 91, 93, 93, 94, 97, 98
There are 8 values in this data set, so we can find the median by taking the average of the two middle values. In this case, the two middle values are 93 and 94:
Median:
(93 + 94) / 2 = 93.5
The median of the data set is 93.5.
To find the mode, we look for the value(s) that appear most frequently in the data set. In this case, we see that both 89 and 93 appear twice, so the data set has two modes:
Modes:
89 and 93
What value best represents all the measures of center for the following data set?
48, 12, 11, 45, 48, 48, 43, 32
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.