Question

The following data represents the high temperatures for the next several days in Buffalo, NY: {17, 26, 3, 13, 20, 34, 30, 41} Find the mean absolute deviation. If necessary round to the nearest hundredth.

Answer 1

To find the mean absolute deviation, you calculate the mean of the data set and then find the absolute difference between each value and the mean. The sum of these absolute differences is divided by the total number of values to find the MAD.

Step-by-step explanation:

To find the mean absolute deviation (MAD), you first calculate the mean (average) of the data set.

The mean of the given temperatures {17, 26, 3, 13, 20, 34, 30, 41} is 22.375.

Then, for each value in the data set, find the absolute difference between that value and the mean.

Sum up all of these absolute differences. Finally, divide the sum by the total number of values in the data set to find the MAD.

Step 1: Calculate the mean: (17+26+3+13+20+34+30+41)/8 = 22.375

Step 2: Find the absolute difference for each value: |17-22.375|+|26-22.375|+|3-22.375|+|13-22.375|+|20-22.375|+|34-22.375|+|30-22.375|+|41-22.375| = 149.625

Step 3: Divide the sum by the number of values: 149.625/8 = 18.703125

Therefore, the mean absolute deviation of the given temperatures is approximately 18.70.