Mean Absolute Deviation Practice

Question

1. Find the mean absolute deviation.
Name.
2. Find the mean absolute deviation.
240, 260, 272, 266, 280, 248
Absolute Data
Mean
Deviation
Deviation
Data
Mean
Deviation
Absolute Deviation
48, 52, 54, 55, 58, 59, 60, 62
3. Find the mean absolute deviation. 3, 15, 6, 54, 7, 38, 10
Data
Mean
Deviation Absolute
Data
Mean Deviation
Absolute Deviation
Sum: Count: Mean Absolute Deviation:

Answer 1

To find the mean absolute deviation (MAD) for a set of data, follow these steps:

1. Calculate the mean (average) of the data.
2. Find the absolute deviations from the mean for each data point (subtract the mean from each data point and take the absolute value of the result).
3. Calculate the mean of the absolute deviations.

Let's go through the provided datasets:

Problem 1

You didn't provide specific numbers, so let's use the information from Problem 2 as an example.

Problem 2: Data Set: 240, 260, 272, 266, 280, 248

1. Calculate the mean. \[ \text{Mean} = \frac{240 + 260 + 272 + 266 + 280 + 248}{6} = \frac{1566}{6} = 261 \]

2. Find the absolute deviations from the mean (261).

   • |240 - 261| = 21
   • |260 - 261| = 1
   • |272 - 261| = 11
   • |266 - 261| = 5
   • |280 - 261| = 19
   • |248 - 261| = 13

   Absolute Deviations: 21, 1, 11, 5, 19, 13

3. Calculate the mean of the absolute deviations. \[ \text{Mean Absolute Deviation} = \frac{21 + 1 + 11 + 5 + 19 + 13}{6} = \frac{70}{6} \approx 11.67 \]

Problem 3: Data Set: 48, 52, 54, 55, 58, 59, 60, 62

1. Calculate the mean. \[ \text{Mean} = \frac{48 + 52 + 54 + 55 + 58 + 59 + 60 + 62}{8} = \frac{388}{8} = 48.5 \]

2. Find the absolute deviations from the mean (55.5).

   • |48 - 55.5| = 7.5
   • |52 - 55.5| = 3.5
   • |54 - 55.5| = 1.5
   • |55 - 55.5| = 0.5
   • |58 - 55.5| = 2.5
   • |59 - 55.5| = 3.5
   • |60 - 55.5| = 4.5
   • |62 - 55.5| = 6.5

   Absolute Deviations: 7.5, 3.5, 1.5, 0.5, 2.5, 3.5, 4.5, 6.5

3. Calculate the mean of the absolute deviations. \[ \text{Mean Absolute Deviation} = \frac{7.5 + 3.5 + 1.5 + 0.5 + 2.5 + 3.5 + 4.5 + 6.5}{8} = \frac{30}{8} = 3.75 \]

Problem 4: Data Set: 3, 15, 6, 54, 7, 38, 10

1. Calculate the mean. \[ \text{Mean} = \frac{3 + 15 + 6 + 54 + 7 + 38 + 10}{7} = \frac{133}{7} \approx 19 \]

2. Find the absolute deviations from the mean (19).

   • |3 - 19| = 16
   • |15 - 19| = 4
   • |6 - 19| = 13
   • |54 - 19| = 35
   • |7 - 19| = 12
   • |38 - 19| = 19
   • |10 - 19| = 9

   Absolute Deviations: 16, 4, 13, 35, 12, 19, 9

3. Calculate the mean of the absolute deviations. \[ \text{Mean Absolute Deviation} = \frac{16 + 4 + 13 + 35 + 12 + 19 + 9}{7} = \frac{108}{7} \approx 15.43 \]

Summary of Results:

• For the dataset 240, 260, 272, 266, 280, 248: MAD ≈ 11.67
• For the dataset 48, 52, 54, 55, 58, 59, 60, 62: MAD = 3.75
• For the dataset 3, 15, 6, 54, 7, 38, 10: MAD ≈ 15.43

Feel free to ask more questions if you need help with any specific calculations or datasets!