What is the outlier in these sets of data?
A 42.5 41.6 42.1 41.9 41.1 42.2
B 39.8 43.6 42.1 40.1 43.9 41.9
C 43.5 42.8 43.8 43.1 42.7 43.3
D 35.0 43.0 37.1 40.5 36.8 42.2
E 42.2 41.6 42.0 41.8 42.6 39.0
In set A, the outlier is 41.1.
In set B, the outlier is 39.8.
In set C, the outlier is 43.5.
In set D, the outlier is 35.0.
In set E, the outlier is 39.0.
To determine the outlier in each set of data, you need to first calculate the mean and standard deviation for each set.
To calculate the mean, sum up all the values in the set and divide by the total number of values. For example, for set A, the mean would be (42.5 + 41.6 + 42.1 + 41.9 + 41.1 + 42.2) / 6 = 42.0667.
To calculate the standard deviation, you can use the following steps:
1. Calculate the difference between each data point and the mean.
2. Square each difference.
3. Calculate the mean of these squared differences.
4. Take the square root of the mean.
After calculating the mean and standard deviation for each set, you can identify the outlier as any value that is more than a certain number of standard deviations away from the mean.
A common rule of thumb is to consider any value that is more than 2 standard deviations away from the mean as an outlier.
Using this rule, you can determine the outliers for each set of data:
A: There are no outliers in set A as all values fall within 2 standard deviations from the mean.
B: The value 43.9 is an outlier in set B as it is more than 2 standard deviations away from the mean.
C: There are no outliers in set C as all values fall within 2 standard deviations from the mean.
D: The value 35.0 is an outlier in set D as it is more than 2 standard deviations away from the mean.
E: There are no outliers in set E as all values fall within 2 standard deviations from the mean.
So, the outliers are 43.9 in set B and 35.0 in set D.
To find the outlier in each set of data, we can use the concept of outliers being values that are significantly different from the other values. One commonly used method is the 1.5 times the interquartile range (IQR) rule.
- For set A:
- Q1 = 41.6, Q3 = 42.2
- IQR = Q3 - Q1 = 42.2 - 41.6 = 0.6
- No values are 1.5 times the IQR away from the Q1 or Q3, so there is no outlier.
- For set B:
- Q1 = 40.1, Q3 = 42.1
- IQR = Q3 - Q1 = 42.1 - 40.1 = 2
- No values are 1.5 times the IQR away from the Q1 or Q3, so there is no outlier.
- For set C:
- Q1 = 42.7, Q3 = 43.5
- IQR = Q3 - Q1 = 43.5 - 42.7 = 0.8
- No values are 1.5 times the IQR away from the Q1 or Q3, so there is no outlier.
- For set D:
- Q1 = 36.8, Q3 = 42.2
- IQR = Q3 - Q1 = 42.2 - 36.8 = 5.4
- The value 35.0 is smaller than Q1 - 1.5 * IQR = 36.8 - 1.5 * 5.4 = 28.9, making it an outlier.
- For set E:
- Q1 = 41.6, Q3 = 42.2
- IQR = Q3 - Q1 = 42.2 - 41.6 = 0.6
- No values are 1.5 times the IQR away from the Q1 or Q3, so there is no outlier.
Therefore, the outlier is 35.0 in set D.