Question

2 a reporter counts the number of times a politician talks about jobs in campaign speeches. what is the mad of the data represented in the dot - plot? number of mentions of \jobs\ a. 1.1 mentions b. 2 mentions c. 2.5 mentions d. 5.5 mentions

Explanation:

Step1: Count data - point frequencies

There is 1 data - point at 3, 1 at 4, 3 at 5, 3 at 6, 1 at 7, 1 at 8. The data set is \(3,4,5,5,5,6,6,6,7,8\).

Step2: Calculate the mean

The sum of the data is \(3 + 4+5\times3 + 6\times3+7 + 8=3 + 4+15 + 18+7 + 8 = 55\). There are \(n = 10\) data - points. The mean \(\bar{x}=\frac{55}{10}=5.5\).

Step3: Calculate the absolute deviations

\(\vert3 - 5.5\vert=2.5\), \(\vert4 - 5.5\vert = 1.5\), \(\vert5 - 5.5\vert=0.5\) (three times), \(\vert6 - 5.5\vert = 0.5\) (three times), \(\vert7 - 5.5\vert=1.5\), \(\vert8 - 5.5\vert = 2.5\).

Step4: Calculate the sum of absolute deviations

The sum is \(2.5+1.5 + 0.5\times3+0.5\times3+1.5+2.5=2.5+1.5 + 1.5+1.5+1.5+2.5 = 11\).

Step5: Calculate the MAD

The MAD (Mean Absolute Deviation) is \(\frac{11}{10}=1.1\).

Answer:

A. 1.1 mentions