Question

1. the following data set represents the number of days emma played soccer each week for the past 5 weeks. 5, 6, 5, 4, 5

number of days distance from mean
5
6
5
4
5
total deviation
a. mean: _______ mad: _______
b. what does the mad represent in the context of the situation?

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{5 + 6+5+4+5}{5}=\frac{25}{5}=5$

Step2: Calculate the distance from the mean for each data - point

For 5: $|5 - 5|=0$
For 6: $|6 - 5|=1$
For 5: $|5 - 5|=0$
For 4: $|4 - 5|=1$
For 5: $|5 - 5|=0$

Step3: Calculate the total deviation

The sum of the distances from the mean is $0 + 1+0+1+0 = 2$

Step4: Calculate the MAD

The Mean Absolute Deviation (MAD) is $\frac{2}{5}=0.4$

Answer:

a. Mean: 5, MAD: 0.4
b. The MAD represents the average distance between each data - point (the number of days Emma played soccer each week) and the mean number of days she played soccer per week. It gives an idea of how spread out the data is around the mean. On average, the number of days Emma played soccer each week deviates from the mean (5 days) by 0.4 days.