Question

Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. Day Sunday Monday Tuesday Wednesday Thursday Friday Saturday Temperature (degrees F) 49 55 52 46 47 42 38 Julia measured the high temperature in her town for one week. Using the chart above, find the mean absolute deviation for the high temperatures. Round your answer to the nearest tenth. Be sure to show your work for finding: the mean of the set of data the distance of each number from the mean the mean absolute deviation

Answer 1

Answer:

$4\dfrac{2}{7}$

Step-by-step explanation:

How to calculate the mean absolute deviation:

Step 1: Calculate the mean.

$\text{Mean}=\dfrac{49+55+52+46+47+42+38}{7}=47$

Step 2: Calculate how far away each data point is from the mean using positive distances. These are called absolute deviations.

$\begin{array}{ccccccc}\text{Sun}&\text{Mon}&\text{Tue}&\text{Wed}&\text{Thu}&\text{Fri}&\text{Sat}\\49&55&52&46&47&42&38\\2&8&5&1&0&5&9\end{array}$

Step 3: Add those deviations together.

$\sum|\text{mean}-x_i|=2+8+4+1+0+5+9=30$

Step 4: Divide the sum by the number of data points.

$\text{MAD}=\dfrac{\sum|\text{mean}-x_i|}{n}=\dfrac{30}{7}=4\dfrac{2}{7}$