Loren’s friends jump as far as they can and record their results in inches. Their results include the observations 42, 47, 50, 42, 45, 41, 49, 51, and 44. Which number, if added to the dataset, would represent an outlier in the data?(1 point)
Responses
72
72
40
40
44
44
52
52
72
To identify an outlier in the dataset, we need to find a number that is significantly different from the other numbers. One common way to determine an outlier is by using the 1.5xIQR rule.
1. Arrange the dataset in ascending order: 41, 42, 42, 44, 45, 47, 49, 50, 51
2. Calculate the interquartile range (IQR) using the formula: IQR = Q3 - Q1
- Q1 is the first quartile (25th percentile)
- Q3 is the third quartile (75th percentile)
3. Calculate Q1 and Q3:
- Q1 = (n + 1) / 4 = (9 + 1) / 4 = 10 / 4 = 2.5
- Q1 is the average of the 2nd and 3rd values: (42 + 42) / 2 = 42
- Q3 = 3 * (n + 1) / 4 = 3 * (9 + 1) / 4 = 3 * 10 / 4 = 7.5
- Q3 is the average of the 7th and 8th values: (47 + 49) / 2 = 48
4. Calculate the IQR: IQR = Q3 - Q1 = 48 - 42 = 6
5. Calculate the lower and upper fences:
- Lower fence = Q1 - 1.5 * IQR = 42 - 1.5 * 6 = 42 - 9 = 33
- Upper fence = Q3 + 1.5 * IQR = 48 + 1.5 * 6 = 48 + 9 = 57
Now we can compare the options given:
- Option 1: 72 - This number is above the upper fence and would be considered an outlier.
- Option 2: 40 - This number is within the range of the dataset.
- Option 3: 44 - This number is already present in the dataset and not an outlier.
- Option 4: 52 - This number is within the range of the dataset.
Therefore, option 1, 72, would represent an outlier in the data.