Sean counted the number of stuffed animals available for prizes in each of the booths at a county fair. The list shows the results.
2, 23, 27, 29, 30, 32, 32, 34, 35, 96
Select all the data values that are outliers.
A.
2
B.
27
C.
34
D.
96
B. 27
D. 96
To identify the outliers, we need to determine if any values are significantly different from the others. One commonly used method is the 1.5 * IQR (interquartile range) rule.
First, we need to find the IQR, which is the range between the first quartile (Q1) and the third quartile (Q3).
Step 1: Arrange the data in ascending order:
2, 23, 27, 29, 30, 32, 32, 34, 35, 96
Step 2: Find Q1 and Q3:
Q1 = 23
Q3 = 34
Step 3: Find the IQR:
IQR = Q3 - Q1
IQR = 34 - 23 = 11
Step 4: Calculate the lower and upper bounds for outliers:
Lower bound = Q1 - 1.5 * IQR
Lower bound = 23 - 1.5 * 11
Lower bound = 23 - 16.5
Lower bound = 6.5
Upper bound = Q3 + 1.5 * IQR
Upper bound = 34 + 1.5 * 11
Upper bound = 34 + 16.5
Upper bound = 50.5
Any values below the lower bound or above the upper bound can be considered outliers.
Looking at the given data, the values 2, 27, and 96 fall outside the range of 6.5 to 50.5.
Therefore, the outliers in the data are:
A. 2
D. 96
To determine if a data value is an outlier, we need to identify values that are significantly different from the other values in the data set.
There are a few methods to determine outliers, one common method being the use of the interquartile range (IQR). The IQR is a measure of statistical dispersion and can help identify values that are significantly higher or lower than the majority of the data.
To find the outliers using the IQR method, follow these steps:
1. Sort the data set in ascending order:
2, 23, 27, 29, 30, 32, 32, 34, 35, 96
2. Find the first quartile (Q1) and the third quartile (Q3).
- Q1 is the median of the lower half of the data set, which is (23 + 27) / 2 = 25
- Q3 is the median of the upper half of the data set, which is (34 + 35) / 2 = 34.5
3. Calculate the IQR by subtracting Q1 from Q3: 34.5 - 25 = 9.5
4. Determine the thresholds for outliers:
- Any value below Q1 - 1.5 * IQR is considered a mild outlier.
- Any value above Q3 + 1.5 * IQR is considered a mild outlier.
In this case, Q1 - 1.5 * IQR = 25 - 1.5 * 9.5 = 10.75
Q3 + 1.5 * IQR = 34.5 + 1.5 * 9.5 = 48.25
Any value below 10.75 or above 48.25 is considered an outlier.
Looking at the data set, we can see that the values 2 and 96 fall outside this range.
Therefore, the outliers in the data set are:
A. 2
D. 96