Question

practice 1 calculate the mad from the data set below: 60, 58, 54, 56, 63, 65, 62, 59, 56, 57

Explanation:

Step1: Find the mean of the data set

First, we sum up all the data points: \(60 + 58 + 54 + 56 + 63 + 65 + 62 + 59 + 56 + 57\)
Let's calculate the sum:
\(60+58 = 118\); \(118+54 = 172\); \(172+56 = 228\); \(228+63 = 291\); \(291+65 = 356\); \(356+62 = 418\); \(418+59 = 477\); \(477+56 = 533\); \(533+57 = 590\)
There are \(n = 10\) data points. So the mean \(\bar{x}=\frac{590}{10}=59\)

Step2: Find the absolute deviations

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

• \(|60 - 59|=1\)
• \(|58 - 59| = 1\)
• \(|54 - 59|=5\)
• \(|56 - 59| = 3\)
• \(|63 - 59|=4\)
• \(|65 - 59| = 6\)
• \(|62 - 59|=3\)
• \(|59 - 59| = 0\)
• \(|56 - 59| = 3\)
• \(|57 - 59| = 2\)

Step3: Find the mean of the absolute deviations

Sum up these absolute deviations: \(1+1 + 5+3+4+6+3+0+3+2\)
Calculate the sum: \(1+1=2\); \(2 + 5=7\); \(7+3 = 10\); \(10+4=14\); \(14+6 = 20\); \(20+3=23\); \(23+0 = 23\); \(23+3=26\); \(26+2 = 28\)
The mean of absolute deviations (MAD) is \(\frac{28}{10}=2.8\)

Answer:

\(2.8\)