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practice 2 calculate the mad from the data set below: 58, 88, 40, 60, 7…

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

First, we sum up all the data points: \(58 + 88 + 40 + 60 + 72 + 66 + 80 + 48\)
\[

$$\begin{align*} &58+88 = 146\\ &146+40 = 186\\ &186+60 = 246\\ &246+72 = 318\\ &318+66 = 384\\ &384+80 = 464\\ &464+48 = 512 \end{align*}$$

\]
There are 8 data points, so the mean \(\bar{x}=\frac{512}{8}=64\)

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

Sum up the absolute deviations: \(6 + 24 + 24 + 4 + 8 + 2 + 16 + 16\)
\[

$$\begin{align*} &6+24 = 30\\ &30+24 = 54\\ &54+4 = 58\\ &58+8 = 66\\ &66+2 = 68\\ &68+16 = 84\\ &84+16 = 100 \end{align*}$$

\]
Now[SSE Completed, Client Connection Error][SSE Completed, Client Connection Error][LLM SSE On Failure]

Answer:

Step1: Find the mean of the data set

First, we sum up all the data points: \(58 + 88 + 40 + 60 + 72 + 66 + 80 + 48\)
\[

$$\begin{align*} &58+88 = 146\\ &146+40 = 186\\ &186+60 = 246\\ &246+72 = 318\\ &318+66 = 384\\ &384+80 = 464\\ &464+48 = 512 \end{align*}$$

\]
There are 8 data points, so the mean \(\bar{x}=\frac{512}{8}=64\)

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

Sum up the absolute deviations: \(6 + 24 + 24 + 4 + 8 + 2 + 16 + 16\)
\[

$$\begin{align*} &6+24 = 30\\ &30+24 = 54\\ &54+4 = 58\\ &58+8 = 66\\ &66+2 = 68\\ &68+16 = 84\\ &84+16 = 100 \end{align*}$$

\]
Now[SSE Completed, Client Connection Error][SSE Completed, Client Connection Error][LLM SSE On Failure]