Question

the table shows the high temperature for the last 6 days. what is the mean absolute deviation for the set of data?

temperature
74 81 65
77 80 75

4
80
6.5

Explanation:

Step1: Calculate the mean

The data set is \(74,81,65,77,80,75\). The mean \(\bar{x}=\frac{74 + 81+65+77+80+75}{6}=\frac{452}{6}\approx75.33\).

Step2: Calculate the absolute - deviations

\(\vert74 - 75.33\vert=1.33\), \(\vert81 - 75.33\vert = 5.67\), \(\vert65 - 75.33\vert=10.33\), \(\vert77 - 75.33\vert = 1.67\), \(\vert80 - 75.33\vert=4.67\), \(\vert75 - 75.33\vert = 0.33\).

Step3: Calculate the mean of the absolute - deviations

The mean absolute deviation \(MAD=\frac{1.33 + 5.67+10.33+1.67+4.67+0.33}{6}=\frac{23.99}{6}\approx4\).

Answer:

4