Question

alg 1.1 lesson 5 redo calculating measures of center and variability
dataset: 12 5 9 7 2
mean: 7

1. calculate the mean absolute deviation (mad) for the data

Explanation:

Step1: Recall MAD formula

The formula for the mean absolute deviation (MAD) is \( \text{MAD} = \frac{1}{n} \sum_{i = 1}^{n} |x_i - \bar{x}| \), where \( n \) is the number of data points, \( x_i \) are the data values, and \( \bar{x} \) is the mean. Here, \( n = 5 \), \( \bar{x}=7 \), and the data points are \( 12, 5, 9, 7, 2 \).

Step2: Calculate absolute deviations

• For \( x_1 = 12 \): \( |12 - 7| = 5 \)
• For \( x_2 = 5 \): \( |5 - 7| = 2 \)
• For \( x_3 = 9 \): \( |9 - 7| = 2 \)
• For \( x_4 = 7 \): \( |7 - 7| = 0 \)
• For \( x_5 = 2 \): \( |2 - 7| = 5 \)

Step3: Sum the absolute deviations

Sum these absolute deviations: \( 5 + 2 + 2 + 0 + 5 = 14 \)

Step4: Divide by number of data points

Now, divide the sum by \( n = 5 \): \( \text{MAD} = \frac{14}{5}= 2.8 \)

Answer:

\( 2.8 \)