Final answer:
To identify outliers in the given data set, we can use the standard deviation. Calculate the mean and standard deviation of the data set. Apply the rule that considers a data point an outlier if it is more than two standard deviations away from the mean. None of the data points in the given data set are outliers.
Step-by-step explanation:
The standard deviation measures how far the data points are spread out from the mean. To identify outliers in a data set, we can use the standard deviation. An outlier is a data point that is significantly different from the other data points. In this case, we have the data set {25, 22, 21, 26, 37, 24, 26, 22}. To find outliers, we can calculate the mean and standard deviation of the data set.
- Calculate the mean: (25+22+21+26+37+24+26+22)/8 = 25.75
- Calculate the standard deviation:
- Subtract the mean from each data point and square the difference: (25-25.75)^2, (22-25.75)^2, (21-25.75)^2, (26-25.75)^2, (37-25.75)^2, (24-25.75)^2, (26-25.75)^2, (22-25.75)^2
- Sum up the squared differences: (0.5625+14.0625+19.0625+0.0625+128.0625+3.5625+0.0625+14.0625) = 179.5
- Divide the sum by the number of data points minus 1: 179.5/(8-1) = 29.92
- Take the square root of the result: sqrt(29.92) ≈ 5.47
- Identify outliers:
- A data point is considered an outlier if it is more than two standard deviations away from the mean.
- In this case, the mean is 25.75 and the standard deviation is approximately 5.47.
- To determine if a data point is an outlier, we can use the following rule: If a data point is less than the mean minus two times the standard deviation or greater than the mean plus two times the standard deviation, it is considered an outlier.
- In our data set, none of the data points satisfy this rule, so we can conclude that there are no outliers.