Finding the Mean in a Data Set

Math

A) To find the mean, we add up all the numbers and divide by the total number of numbers:

5 + 7 + 3 + 8 + 2 + 3 + 3 + 1 + 9 = 41

There are 9 numbers in the list, so the mean is:

mean = 41/9 ? 4.56

To find the median, we first need to put the numbers in order from smallest to largest:

1, 2, 3, 3, 3, 5, 7, 8, 9

There are 9 numbers in the list, so the median is the middle number, which is:

median = 3

To find the mode, we look for the number that appears most often in the list. In this case, there is one number that appears three times, so the mode is:

mode = 3

B) To find the mean, we add up all the numbers and divide by the total number of numbers:

104 + 139 + 145 + 150 + 167 + 205 + 205 + 20 = 1135

There are 8 numbers in the list, so the mean is:

mean = 1135/8 ? 141.88

To find the median, we first need to put the numbers in order from smallest to largest:

20, 104, 139, 145, 150, 167, 205, 205

There are 8 numbers in the list, so the median is the average of the two middle numbers, which are:

median = (145 + 150)/2 = 147.5

To find the mode, we look for the number that appears most often in the list. In this case, 205 appears twice, which is more than any other number, so the mode is:

mode = 205

C) To find the mean, we first need to reconstruct the list of numbers. Each stem corresponds to a ten\'s place, and each leaf corresponds to a one\'s place. For example, the first row in the stem and leaf plot corresponds to the numbers 10, 13, 15, and 15. So the reconstructed list is:

10, 13, 15, 15, 20, 21, 24, 27, 27, 27, 27, 28, 28, 29, 33, 33, 35, 38, 39, 40, 41, 57, 58, 58, 58, 59, 59

To find the mean, we add up all the numbers and divide by the total number of numbers:

10 + 13 + 15 + 15 + 20 + 21 + 24 + 27 + 27 + 27 + 27 + 28 + 28 + 29 + 33 + 33 + 35 + 38 + 39 + 40 + 41 + 57 + 58 + 58 + 58 + 59 + 59 = 862

There are 27 numbers in the list, so the mean is:

mean = 862/27 ? 31.93