Question

bryce volunteered to stamp hands at the entrance of a museum 7 times this year. the number of visitors each time was: 9 visitors 5 visitors 9 visitors 3 visitors 7 visitors 8 visitors 1 visitor what was the mean absolute deviation of the numbers of visitors? if the answer is a decimal, round it to the nearest tenth. mean absolute deviation (mad): \boxed{} visitors

Explanation:

Step1: Calculate the mean

First, find the sum of the number of visitors: \(9 + 5 + 9 + 3 + 7 + 8 + 1 = 42\).
There are 7 data points, so the mean \(\bar{x}=\frac{42}{7}=6\).

Step2: Find absolute deviations

Calculate the absolute deviation of each data point from the mean:

• \(|9 - 6| = 3\)
• \(|5 - 6| = 1\)
• \(|9 - 6| = 3\)
• \(|3 - 6| = 3\)
• \(|7 - 6| = 1\)
• \(|8 - 6| = 2\)
• \(|1 - 6| = 5\)

Step3: Calculate the mean of absolute deviations

Sum these absolute deviations: \(3 + 1 + 3 + 3 + 1 + 2 + 5 = 18\).
Then divide by the number of data points (7): \(\text{MAD}=\frac{18}{7}\approx2.6\) (rounded to the nearest tenth).

Answer:

2.6