Sarina tracks her time spent on homework each night for a week, in minutes. She collects the following times: 51, 60, 25, 15, 20, 5, 35. When she solves for the mean absolute deviation, what number will she use for the divisor?
To find the mean absolute deviation, we first need to find the mean of the data set. The mean is found by adding up all the values and dividing by the total number of values. In this case, the sum of the values is 51 + 60 + 25 + 15 + 20 + 5 + 35 = 211. There are 7 values in the data set, so we divide the sum by 7 to find the mean: 211/7 = <<211/7=30.14>>30.14.
The divisor for the mean absolute deviation is the mean, which is 30.14.
To find the mean absolute deviation (MAD), Sarina will need to find the average of the absolute differences between each data point and the mean.
First, let's find the mean (average) of the data set.
Mean = (51 + 60 + 25 + 15 + 20 + 5 + 35) / 7 = 211 / 7 ≈ 30.14
The mean is approximately 30.14.
Next, she will need to find the absolute differences between each data point and the mean.
Absolute difference = |Data point - Mean|
For example, the absolute difference for the first data point (51) would be |51 - 30.14| = 20.86.
Summing up the absolute differences for all data points, we get:
|51 - 30.14| + |60 - 30.14| + |25 - 30.14| + |15 - 30.14| + |20 - 30.14| + |5 - 30.14| + |35 - 30.14|
= 20.86 + 29.86 + 5.14 + 15.14 + 10.14 + 25.14 + 4.86
= 111.04
The sum of the absolute differences is 111.04.
Finally, to find the MAD, she will divide the sum of the absolute differences by the number of data points. In this case, there are 7 data points.
MAD = Sum of absolute differences / Number of data points = 111.04 / 7 ≈ 15.86
Therefore, she will use the number 7 as the divisor when calculating the mean absolute deviation.