MATH 7 B: DISPLAYING AND ANALYZING DATA UNIT

Question

Be sure to save this worksheet and use it in the lessons that include instructions for your unit portfolio. Follow the directions in the lessons to complete each component of your project. Complete each part of the analysis when prompted in a lesson. Submit the complete analysis at the end of the unit. Data Set: Number of Pages in the Selected Books

pages in book 1: 256
pages in book 2: 384
pages in book 3: 31
pages in book 4: 24
pages in book 5: 384
pages in book 6: 64
pages in book 7: 45
pages in book 8: 33
pages in book 9: 22
pages in book 10: 59
pages in book 11: 144
pages in book 12: 273
pages in book 13: 171
pages in book 14: 88
pages in book 15: 210

Find the mean absolute deviation (MAD)

Answer 1

To find the mean absolute deviation (MAD), follow these steps:

1. Find the mean of the data set:
Add up all the values and divide by the number of values:
(256+384+31+24+384+64+45+33+22+59+144+273+171+88+210) / 15 = 137.6

2. Calculate the deviation from the mean for each value:
Subtract the mean (137.6) from each value in the data set:
256-137.6 = 118.4
384-137.6 = 246.4
31-137.6 = -106.6
24-137.6 = -113.6
384-137.6 = 246.4
64-137.6 = -73.6
45-137.6 = -92.6
33-137.6 = -104.6
22-137.6 = -115.6
59-137.6 = -78.6
144-137.6 = 6.4
273-137.6 = 135.4
171-137.6 = 33.4
88-137.6 = -49.6
210-137.6 = 72.4

3. Find the absolute value of each deviation:
Ignore the negative signs by taking the absolute value of each deviation:
|118.4| = 118.4
|246.4| = 246.4
|-106.6| = 106.6
|-113.6| = 113.6
|246.4| = 246.4
|-73.6| = 73.6
|-92.6| = 92.6
|-104.6| = 104.6
|-115.6| = 115.6
|-78.6| = 78.6
|6.4| = 6.4
|135.4| = 135.4
|33.4| = 33.4
|-49.6| = 49.6
|72.4| = 72.4

4. Find the average of the absolute deviations:
Add up all the absolute deviations and divide by the number of values:
(118.4+246.4+106.6+113.6+246.4+73.6+92.6+104.6+115.6+78.6+6.4+135.4+33.4+49.6+72.4) / 15 ≈ 96.1

The mean absolute deviation (MAD) of the data set is approximately 96.1.