The mean deviation from the means of the data [tex]$13,13,13,13,13$[/tex] is...
A) 0
B) 1
C) 13
Answer (2)
The mean deviation from the means of the data set [ 13 , 13 , 13 , 13 , 13 ] is calculated to be 0, as all data points are equal to the mean. Therefore, the answer is A) 0.
;
Calculate the mean of the data set: 5 13 + 13 + 13 + 13 + 13 = 13 .
Find the absolute deviation of each data point from the mean: ∣13 − 13∣ = 0 for all data points.
Calculate the mean of the absolute deviations: 5 0 + 0 + 0 + 0 + 0 = 0 .
The mean deviation from the mean is 0 .
Explanation
Analyze the data First, let's analyze the given data. We have a data set consisting of five identical numbers: 13 , 13 , 13 , 13 , 13 . Our goal is to find the mean deviation from the mean for this data set. This involves finding the mean of the data, calculating the absolute deviations of each data point from the mean, and then finding the mean of those absolute deviations.
Calculate the mean Next, we calculate the mean of the data set. Since all the numbers are the same, the mean is simply 13. We can calculate it as follows: Mean = 5 13 + 13 + 13 + 13 + 13 = 5 65 = 13
Find the absolute deviations Now, we find the absolute deviation of each data point from the mean. The absolute deviation is the absolute value of the difference between each data point and the mean. In this case, since every data point is equal to the mean (13), the absolute deviation for each point is ∣13 − 13∣ = 0 .
Calculate the mean deviation Then, we calculate the mean of the absolute deviations. Since all the absolute deviations are 0, the mean of the absolute deviations is also 0. We calculate it as follows: Mean Deviation = 5 0 + 0 + 0 + 0 + 0 = 5 0 = 0
State the final answer Therefore, the mean deviation from the mean of the data set 13 , 13 , 13 , 13 , 13 is 0.
Examples
The mean absolute deviation is a measure of statistical dispersion. It helps to understand how spread out the data points are from the average value. In fields like finance, it can be used to assess the risk associated with investments by measuring the deviation of returns from the average return. For example, if a stock's returns are consistently close to its average, the mean absolute deviation will be low, indicating lower risk.
