Question
A 5-number summary gives the values 3, 6, 8, 12, and 18. Which two numbers in the summary are used to identify if there are any outliers?(1 point)
Responses
The median alone can identify that there are no outliers in this dataset.
The median alone can identify that there are no outliers in this dataset. - no response given
The median of 6 and the IQR of 6 are used to calculate that there are two outliers in this dataset.
The median of 6 and the IQR of 6 are used to calculate that there are two outliers in this dataset. - no response given
The upper and lower quartiles of 12 and 6 and the IQR of 6 are used to calculate that there are no outliers in this dataset.
The upper and lower quartiles of 12 and 6 and the IQR of 6 are used to calculate that there are no outliers in this dataset. - no response given
The maximum and minimum values of 18 and 3 are used to calculate that there are two outliers in this dataset.
Responses
The median alone can identify that there are no outliers in this dataset.
The median alone can identify that there are no outliers in this dataset. - no response given
The median of 6 and the IQR of 6 are used to calculate that there are two outliers in this dataset.
The median of 6 and the IQR of 6 are used to calculate that there are two outliers in this dataset. - no response given
The upper and lower quartiles of 12 and 6 and the IQR of 6 are used to calculate that there are no outliers in this dataset.
The upper and lower quartiles of 12 and 6 and the IQR of 6 are used to calculate that there are no outliers in this dataset. - no response given
The maximum and minimum values of 18 and 3 are used to calculate that there are two outliers in this dataset.
Answers
Answered by
GPT-4o mini
To identify outliers in a dataset using the 5-number summary, you typically focus on the lower quartile (Q1), upper quartile (Q3), and the interquartile range (IQR). In the case of the provided 5-number summary (3, 6, 8, 12, 18), the pertinent values are:
- Q1 (lower quartile): 6
- Q3 (upper quartile): 12
- IQR: Q3 - Q1 = 12 - 6 = 6
Outliers can be identified using the following formulas:
- Lower bound: Q1 - 1.5 * IQR
- Upper bound: Q3 + 1.5 * IQR
Calculating the bounds:
- Lower bound: 6 - 1.5 * 6 = 6 - 9 = -3
- Upper bound: 12 + 1.5 * 6 = 12 + 9 = 21
With these bounds, any data point below -3 or above 21 would be considered an outlier. Since the maximum is 18 and the minimum is 3, there are no outliers in this dataset.
Thus, the correct response regarding the two numbers used to identify outliers is:
"The upper and lower quartiles of 12 and 6 and the IQR of 6 are used to calculate that there are no outliers in this dataset."
- Q1 (lower quartile): 6
- Q3 (upper quartile): 12
- IQR: Q3 - Q1 = 12 - 6 = 6
Outliers can be identified using the following formulas:
- Lower bound: Q1 - 1.5 * IQR
- Upper bound: Q3 + 1.5 * IQR
Calculating the bounds:
- Lower bound: 6 - 1.5 * 6 = 6 - 9 = -3
- Upper bound: 12 + 1.5 * 6 = 12 + 9 = 21
With these bounds, any data point below -3 or above 21 would be considered an outlier. Since the maximum is 18 and the minimum is 3, there are no outliers in this dataset.
Thus, the correct response regarding the two numbers used to identify outliers is:
"The upper and lower quartiles of 12 and 6 and the IQR of 6 are used to calculate that there are no outliers in this dataset."