Question

practice 2 calculate the mad from the data set below: 58,88,40,60,72,66,80,48

Explanation:

Step1: Find the mean of the data set.

The data set is \(58, 88, 40, 60, 72, 66, 80, 48\). The number of data points \(n = 8\).
The mean \(\bar{x}=\frac{58 + 88+40 + 60+72 + 66+80 + 48}{8}\)
First, calculate the sum: \(58+88 = 146\), \(146+40 = 186\), \(186+60 = 246\), \(246+72 = 318\), \(318+66 = 384\), \(384+80 = 464\), \(464+48 = 512\).
Then, \(\bar{x}=\frac{512}{8}=64\).

Step2: Find the absolute deviations from the mean.

For each data point \(x_i\), calculate \(|x_i-\bar{x}|\):

• \(|58 - 64|=6\)
• \(|88 - 64|=24\)
• \(|40 - 64|=24\)
• \(|60 - 64|=4\)
• \(|72 - 64|=8\)
• \(|66 - 64|=2\)
• \(|80 - 64|=16\)
• \(|48 - 64|=16\)

Step3: Find the mean of these absolute deviations (MAD).

Sum of absolute deviations: \(6 + 24+24 + 4+8 + 2+16 + 16\)
Calculate the sum: \(6+24 = 30\), \(30+24 = 54\), \(54+4 = 58\), \(58+8 = 66\), \(66+2 = 68\), \(68+16 = 84\), \(84+16 = 100\).
MAD \(=\frac{100}{8}=12.5\)

Answer:

\(12.5\)