Question

question 2 (1 point)
a reporter counts the number of times a politician talks about jobs in their campaign speeches. what is the mad of the data represented in the dot plot?
2 3 4 5 6 7 8 9
number of mentions of \jobs\
a 5.5 mentions
b 1.1 mentions
c 2.5 mentions
d 2 mentions

Explanation:

Step1: Count data - points

There are 8 data - points: 3, 4, 5, 5, 5, 6, 6, 6, 7, 8.

Step2: Calculate the mean

$\bar{x}=\frac{3 + 4+5\times3 + 6\times3+7 + 8}{8}=\frac{3 + 4+15+18+7 + 8}{8}=\frac{55}{8}=6.875$.

Step3: Calculate absolute deviations

$|3 - 6.875| = 3.875$, $|4 - 6.875| = 2.875$, $|5 - 6.875| = 1.875$ (three times), $|6 - 6.875| = 0.875$ (three times), $|7 - 6.875| = 0.125$, $|8 - 6.875| = 1.125$.

Step4: Calculate the sum of absolute deviations

$S=3.875+2.875 + 3\times1.875+3\times0.875+0.125+1.125$
$=3.875+2.875+5.625 + 2.625+0.125+1.125=16$.

Step5: Calculate the MAD

$MAD=\frac{S}{n}=\frac{16}{8}=2$.

Answer:

d. 2 mentions