Question

the data set shows the number of people who attended the last 8 town meetings. 62, 70, 58, 76, 84, 110, 86, 54. what happens to the mad if 39 is added to the data set? enter the answer. the mad increases to

Explanation:

Step1: Calculate the mean of the original data - set

The original data - set is \(62,70,58,76,84,110,86,54\).
The sum of the data is \(62 + 70+58 + 76+84+110+86+54=600\).
The number of data points \(n = 8\).
The mean \(\bar{x}=\frac{600}{8}=75\).

Step2: Calculate the absolute - deviations of the original data - set

\(\vert62 - 75\vert=13\), \(\vert70 - 75\vert = 5\), \(\vert58 - 75\vert=17\), \(\vert76 - 75\vert = 1\), \(\vert84 - 75\vert=9\), \(\vert110 - 75\vert=35\), \(\vert86 - 75\vert=11\), \(\vert54 - 75\vert=21\).
The sum of the absolute - deviations is \(13 + 5+17+1+9+35+11+21 = 112\).
The mean absolute deviation (MAD) of the original data - set is \(\text{MAD}_1=\frac{112}{8}=14\).

Step3: Add 39 to the data - set and calculate the new mean

The new data - set is \(62,70,58,76,84,110,86,54,39\).
The sum of the new data is \(600+39 = 639\).
The number of data points \(n = 9\).
The new mean \(\bar{y}=\frac{639}{9}=71\).

Step4: Calculate the absolute - deviations of the new data - set

\(\vert62 - 71\vert=9\), \(\vert70 - 71\vert = 1\), \(\vert58 - 71\vert=13\), \(\vert76 - 71\vert = 5\), \(\vert84 - 71\vert=13\), \(\vert110 - 71\vert=39\), \(\vert86 - 71\vert=15\), \(\vert54 - 71\vert=17\), \(\vert39 - 71\vert=32\).
The sum of the absolute - deviations is \(9+1+13+5+13+39+15+17+32 = 144\).
The new mean absolute deviation (MAD) is \(\text{MAD}_2=\frac{144}{9}=16\).

Answer:

16