Question

What is the mean absolute deviation of the dataset: 125, 198, 209, 213, 101, and 178?

A) 30
B) 37
C) 42
D) 56

Answer 1

The mean absolute deviation of the dataset is calculated to be approximately 38.39, which is closest to option B) 37.

Step-by-step explanation:

To calculate the mean absolute deviation of a dataset, follow these steps:

1. First, find the mean (average) of the dataset.
2. Then, subtract the mean from each data value to find the deviations.
3. Take the absolute value of each deviation.
4. Finally, find the mean of these absolute values.

The dataset is: 125, 198, 209, 213, 101, and 178.

Calculating the mean:

(125 + 198 + 209 + 213 + 101 + 178) / 6 = 1024 / 6

= 170.67 (rounded to 2 decimal places)

Now, find the deviations and their absolute values:

• |125 - 170.67| = 45.67
• |198 - 170.67| = 27.33
• |209 - 170.67| = 38.33
• |213 - 170.67| = 42.33
• |101 - 170.67| = 69.67
• |178 - 170.67| = 7.33

Find the mean of these absolute values:

(45.67 + 27.33 + 38.33 + 42.33 + 69.67 + 7.33) / 6 = 230.36 / 6

= 38.39

Therefore, the mean absolute deviation of the dataset is approximately 38.39, which is closest to option B) 37.