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

1. calculate the interquartile range (iqr) for the data

Explanation:

1) Calculating Mean Absolute Deviation (MAD)

Step1: Find absolute deviations

For each data point \( x \), calculate \( |x - \text{mean}| \). Mean is 7.

• \( |12 - 7| = 5 \)
• \( |5 - 7| = 2 \)
• \( |9 - 7| = 2 \)
• \( |7 - 7| = 0 \)
• \( |2 - 7| = 5 \)

Step2: Calculate mean of deviations

Sum the absolute deviations: \( 5 + 2 + 2 + 0 + 5 = 14 \). Divide by number of data points (5): \( \frac{14}{5} = 2.8 \).

Step1: Order the data

Ordered dataset: \( 2, 5, 7, 9, 12 \).

Step2: Find Q1 and Q3

• Q1 (median of lower half): Lower half is \( 2, 5 \). Median is \( \frac{2 + 5}{2} = 3.5 \).
• Q3 (median of upper half): Upper half is \( 9, 12 \). Median is \( \frac{9 + 12}{2} = 10.5 \).

Step3: Calculate IQR

IQR = Q3 - Q1 = \( 10.5 - 3.5 = 7 \).

Answer:

The mean absolute deviation (MAD) is \( 2.8 \).

2) Calculating Interquartile Range (IQR)