based on the provided summary statistics, there is an outlier at the lower end of the data (option B). Therefore, B:There is an outlier at the lower end of the data.
Based on the summary statistics provided, the interquartile range (IQR) can be calculated:
IQR = Q3 - Q1 = 76 - 57 = 19
Typically, outliers can be identified using the following rule:
Values below Q1 - 1.5 * IQR or above Q3 + 1.5 * IQR can be considered outliers.
Let's calculate these values:
Below Q1 - 1.5 * IQR = 57 - 1.5 * 19 = 57 - 28.5 = 28.5
Above Q3 + 1.5 * IQR = 76 + 1.5 * 19 = 76 + 28.5 = 104.5
According to this rule:
The minimum value is 12, which is below 28.5, so it can be considered an outlier on the lower end.
The maximum value is 100, which is not above 104.5, so it's not considered an outlier on the upper end.
So, based on the provided summary statistics, there is an outlier at the lower end of the data (option B).
Question
To keep some privacy about the students, a professor releases only summary statistics about student scores on a difficult quiz.
mean- 66.91 standard deviation - 12.74 minimum - 12 Q1 - 57 median -66 Q3- 76 maximum-100
Based on this information, what can you know about outliers in the student scores?
A:There is an outlier at the upper end of the data.
B:There is an outlier at the lower end of the data.
C:There are outliers on both ends of the data.
D: There is not enough information to determine whether there are any outliers.