MATH 7 B: DISPLAYING AND ANALYZING DATA UNIT

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)

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.

To find the Mean Absolute Deviation (MAD), follow these steps:

Step 1: Find the mean (average) of the data set.
Step 2: Subtract the mean from each data value to find the deviations.
Step 3: Take the absolute value of each deviation.
Step 4: Find the average of these absolute deviations.

Let's calculate the MAD for the given data set:

Step 1: Find the mean (average):
Sum of all pages = 256 + 384 + 31 + 24 + 384 + 64 + 45 + 33 + 22 + 59 + 144 + 273 + 171 + 88 + 210 = 2473

Number of books = 15

Mean = Sum of all pages / Number of books = 2473 / 15 ≈ 164.87

Step 2: Subtract the mean from each data value to find the deviations:
Deviation for book 1 = 256 - 164.87 ≈ 91.13
Deviation for book 2 = 384 - 164.87 ≈ 219.13
Deviation for book 3 = 31 - 164.87 ≈ -133.87
Deviation for book 4 = 24 - 164.87 ≈ -140.87
Deviation for book 5 = 384 - 164.87 ≈ 219.13
Deviation for book 6 = 64 - 164.87 ≈ -100.87
Deviation for book 7 = 45 - 164.87 ≈ -119.87
Deviation for book 8 = 33 - 164.87 ≈ -131.87
Deviation for book 9 = 22 - 164.87 ≈ -142.87
Deviation for book 10 = 59 - 164.87 ≈ -105.87
Deviation for book 11 = 144 - 164.87 ≈ -20.87
Deviation for book 12 = 273 - 164.87 ≈ 108.13
Deviation for book 13 = 171 - 164.87 ≈ 6.13
Deviation for book 14 = 88 - 164.87 ≈ -76.87
Deviation for book 15 = 210 - 164.87 ≈ 45.13

Step 3: Take the absolute value of each deviation:
Absolute deviation for book 1 ≈ |91.13| = 91.13
Absolute deviation for book 2 ≈ |219.13| = 219.13
Absolute deviation for book 3 ≈ |-133.87| = 133.87
Absolute deviation for book 4 ≈ |-140.87| = 140.87
Absolute deviation for book 5 ≈ |219.13| = 219.13
Absolute deviation for book 6 ≈ |-100.87| = 100.87
Absolute deviation for book 7 ≈ |-119.87| = 119.87
Absolute deviation for book 8 ≈ |-131.87| = 131.87
Absolute deviation for book 9 ≈ |-142.87| = 142.87
Absolute deviation for book 10 ≈ |-105.87| = 105.87
Absolute deviation for book 11 ≈ |-20.87| = 20.87
Absolute deviation for book 12 ≈ |108.13| = 108.13
Absolute deviation for book 13 ≈ |6.13| = 6.13
Absolute deviation for book 14 ≈ |-76.87| = 76.87
Absolute deviation for book 15 ≈ |45.13| = 45.13

Step 4: Find the average of these absolute deviations:
Sum of absolute deviations = 91.13 + 219.13 + 133.87 + 140.87 + 219.13 + 100.87 + 119.87 + 131.87 + 142.87 + 105.87 + 20.87 + 108.13 + 6.13 + 76.87 + 45.13 = 1548.92

MAD = Sum of absolute deviations / Number of books = 1548.92 / 15 ≈ 103.26

Therefore, the Mean Absolute Deviation (MAD) for the given data set is approximately 103.26 pages.

To find the Mean Absolute Deviation (MAD), follow these steps:

Step 1: Calculate the mean of the data set.
To find the mean, add up all the values in the data set and divide the sum by the total number of values.

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

Mean = (256 + 384 + 31 + 24 + 384 + 64 + 45 + 33 + 22 + 59 + 144 + 273 + 171 + 88 + 210) / 15
Mean = 2480 / 15
Mean = 165.33 (rounded to two decimal places)

Step 2: Calculate the absolute deviation from the mean for each value.
Absolute deviation is the absolute difference between each data value and the mean.

Absolute deviation for book 1: |256 - 165.33| = 90.67
Absolute deviation for book 2: |384 - 165.33| = 218.67
Absolute deviation for book 3: |31 - 165.33| = 134.33
...
Absolute deviation for book 15: |210 - 165.33| = 44.67

Step 3: Calculate the average of the absolute deviations.
To find the MAD, add up all the absolute deviations and divide the sum by the total number of values.

MAD = (90.67 + 218.67 + 134.33 + ... + 44.67) / 15

MAD = sum_of_absolute_deviations / 15

After calculating the sum of the absolute deviations, divide the result by 15 to find the MAD.