Question

28, 45, 12, 34, 36, 45, 19,20

Answer 1

Part A

To find the mean, we add up the values and divide by n = 8 since there are 8 values in this set.

Adding the values gets us

28+45+12+34+36+45+19+20 = 239

Dividing this over 8 then leads to 239/8 = 29.875

Answer: 29.875

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Part B

We'll subtract each data value from the mean. We apply absolute value to ensure the result is never negative.

• |28 - 29.875| = 1.875
• |45 - 29.875| = 15.125
• |12 - 29.875| = 17.875
• |34 - 29.875| = 4.125
• |36 - 29.875| = 6.125
• |45 - 29.875| = 15.125
• |19 - 29.875| = 10.875
• |20 - 29.875| = 9.875

The list of results we get so far is:

1.875, 15.125, 17.875, 4.125, 6.125, 15.125, 10.875, 9.875

This represents the distance each value is from the mean.

Add these values up and divide by n = 8

1.875+15.125+17.875+4.125+6.125+15.125+10.875+9.875 = 81

81/8 = 10.125

Answer: 10.125

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Part C

The result of part A is one way to measure the center of the distribution of values. It's the average value, which can more or less represent the entire group. Think of it being like how people vote in a senator to represent them in congress. Ideally, this senator is a supposed "average" person to represent everyone.

The result of part B builds on what part A found. The result of part B is the average distance each value is from the center. This is because each time we subtracted and applied absolute value, we found the distance that item was from the mean.

Example: The calculation |28 - 29.875| = 1.875 shows that 28 is exactly 1.875 units from the mean 29.875

By adding up those results and dividing by 8, we are finding the average distance from the mean. Effectively, it tells us how spread out the data set is. The mean absolute deviation (MAD) is a measure of spread in a similar fashion that the standard deviation is, or in a more looser sense, the range is as well.

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In short, the result of part A is a measure of center while the result of part B is a measure of spread. I use "a" instead of "the" because there are other measures of center and other measures of spread.