Question

Wats is MAD 99,45,23,67,45,91,82,78,62,51

Answer 1

To find the Mean Absolute Deviation (MAD) of the dataset \(99, 45, 23, 67, 45, 91, 82, 78, 62, 51\), follow these steps:

1. **Calculate the Mean:**
\[
\text{Mean} = \frac{\text{Sum of all data points}}{\text{Number of data points}}
\]
\[
\text{Mean} = \frac{99 + 45 + 23 + 67 + 45 + 91 + 82 + 78 + 62 + 51}{10} = \frac{ 99 + 45 + 23 + 67 + 45 + 91 + 82 + 78 + 62 + 51}{10} = \frac{ 99 + 45 + 23 + 67 + 45 + 91 + 82 + 78 + 62 + 51}{10} = \frac{ 45 + 67 + 99 + 23 + 55 + 78 + 91 + 82 + 62 + 51}{10}= \frac{651}{10} = 65.1
\]

2. **Calculate the Absolute Deviations:**
Subtract the mean from each data point and take the absolute value:
\[
|99 - 65.1| = 33.9
\]
\[
|45 - 65.1| = 20.1
\]
\[
|23 - 65.1| = 42.1
\]
\[
|67 - 65.1| = 1.9
\]
\[
|45 - 65.1| = 20.1
\]
\[
|91 - 65.1| = 25.9
\]
\[
|82 - 65.1| = 16.9
\]
\[
|78 - 65.1| = 12.9
\]
\[
|62 - 65.1| = 3.1
\]
\[
|51 - 65.1| = 14.1
\]

3. **Calculate the Mean Absolute Deviation:**
Now sum these absolute deviations and divide by the number of data points:
\[
\text{MAD} = \frac{|99 - 65.1| + |45 - 65.1| + |23 - 65.1| + |67 - 65.1| + |45 - 65.1| + |91 - 65.1| + |82 - 65.1| + |78 - 65.1| + |62 - 65.1| + |51 - 65.1|}{10}
\]
\[
= \frac{33.9 + 20.1 + 42.1 + 1.9 + 20.1 + 25.9 + 16.9 + 12.9 + 3.1 + 14.1}{10}
\]
\[
= \frac{ %Data%}{10}
\]
\[
= \frac{ 33.9 + 20.1 + 42.1 + 1.9 + 20.1 + 25.9 + 16.9 + 12.9 + 3.1 + 14.1}{10.}
= \frac{ 77. 13.4 + + %Data% + 1.9 + 20.1 + 25.9 + 16.9 + 12.9 + 3.1 + 14.1}{10} ≈ 18.51
\]

Hence, the Mean Absolute Deviation (MAD) of the dataset is approximately \( 18.51 \).