Question
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
40
40
44
44
72
72
52
The number that, if added to the dataset, would represent an outlier in the data is:
72
To determine which number would represent an outlier in the dataset, you need to identify any data point that significantly differs from the other values. One common method for identifying outliers is through the use of the interquartile range (IQR).
1. First, arrange the dataset in ascending order: 41, 42, 42, 44, 45, 47, 49, 50, 51.
2. Calculate the IQR: The IQR is the range between the 25th percentile (Q1) and the 75th percentile (Q3) of the dataset.
a. Determine the position of Q1 and Q3:
- Q1 = position (n+1)/4 = (9+1)/4 = 10/4 = 2.5 (interpolated)
- Q3 = 3*(n+1)/4 = 3*(9+1)/4 = 3*10/4 = 30/4 = 7.5 (interpolated)
b. Find the values that correspond to Q1 and Q3:
- Q1 = (42+44)/2 = 43
- Q3 = (49+50)/2 = 49.5
c. Calculate the IQR: IQR = Q3 - Q1 = 49.5 - 43 = 6.5
3. Evaluate each data point to determine if it is an outlier:
- Any data point below Q1 - 1.5*(IQR) or above Q3 + 1.5*(IQR) is considered an outlier.
- Lower outlier boundary: Q1 - 1.5*(IQR) = 43 - 1.5*(6.5) = 43 - 9.75 = 33.25
- Upper outlier boundary: Q3 + 1.5*(IQR) = 49.5 + 1.5*(6.5) = 49.5 + 9.75 = 59.25
4. Compare each option with the outlier boundaries:
- Option 1: 40 is below the lower outlier boundary (33.25). It would be considered an outlier.
- Option 2: 44 is within the range of the dataset and is not considered an outlier.
- Option 3: 72 is above the upper outlier boundary (59.25). It would be considered an outlier.
- Option 4: 52 is within the range of the dataset and is not considered an outlier.
Based on this analysis, the option that would represent an outlier in the data is 40.