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
To determine which number would represent an outlier in the data, we need to calculate the interquartile range (IQR) and identify any values that fall outside of the range.
First, we need to arrange the data in ascending order:
41, 42, 42, 44, 45, 47, 49, 50, 51
Next, we can calculate the first quartile (Q1), third quartile (Q3), and the IQR:
Q1 = 42
Q3 = 49
IQR = Q3 - Q1 = 49 - 42 = 7
Using the IQR, we can identify any values that fall outside of the range:
Lower fence = Q1 - (1.5 * IQR) = 42 - (1.5 * 7) = 31.5
Upper fence = Q3 + (1.5 * IQR) = 49 + (1.5 * 7) = 59.5
Any value that is less than the lower fence or greater than the upper fence would be considered an outlier.
Comparing the given options:
1. 40 falls within the range and is not an outlier.
2. 44 is already included in the dataset and is not an outlier.
3. 72 is greater than the upper fence and would be considered an outlier.
4. 52 falls within the range and is not an outlier.
Therefore, the number that would represent an outlier in the data is 72.
To determine which number, if added to the dataset, would represent an outlier, we need to identify values that are significantly different from the rest of the data.
To do this, we can calculate the interquartile range (IQR), which is the range between the first quartile (Q1) and the third quartile (Q3). Any value that is more than 1.5 times the IQR away from the nearest quartile is considered an outlier.
First, let's arrange the dataset in ascending order: 41, 42, 42, 44, 45, 47, 49, 50, 51.
Next, we calculate Q1 and Q3. Since the dataset has an odd number of values, we can find Q1 by taking the median of the lower half and Q3 by taking the median of the upper half.
Q1 = (42 + 42) / 2 = 42
Q3 = (49 + 50) / 2 = 49.5
Next, we calculate the IQR:
IQR = Q3 - Q1 = 49.5 - 42 = 7.5
To find the potential outliers, we can check for values that are more than 1.5 times the IQR away from Q1 or Q3.
Lower Outlier Threshold: Q1 - 1.5 * IQR = 42 - 1.5 * 7.5 = 42 - 11.25 = 30.75
Upper Outlier Threshold: Q3 + 1.5 * IQR = 49.5 + 1.5 * 7.5 = 49.5 + 11.25 = 60.75
Now, let's examine the given options: 40, 44, 72, 52.
- 40 is less than the lower outlier threshold (30.75). Therefore, it is a potential outlier.
- 44 is within the range (between Q1 and Q3) and is not an outlier.
- 72 is greater than the upper outlier threshold (60.75). Therefore, it is a potential outlier.
- 52 is greater than the upper outlier threshold (60.75). Therefore, it is a potential outlier.
Based on this analysis, both 40 and 72 would represent outliers if added to the dataset.