Answer :
None of the values in the given sample (37, 82, 24, 25, 31, 10, 41, 44, 4, 36, 68) will be labeled as outliers in the boxplot. Option l
To determine which values, if any, will be labeled as outliers in a boxplot, calculate the quartiles and the interquartile range (IQR).
Given the sample: 37, 82, 24, 25, 31, 10, 41, 44, 4, 36, 68.
Arrange the sample in ascending order: 4, 10, 24, 25, 31, 36, 37, 41, 44, 68, 82.
Calculate the first quartile (Q1):
The median of the lower half of the data set.
In this case, the lower half is: 4, 10, 24, 25, 31.
Q1 = median of the lower half = (24 + 25) / 2 = 24.5.
Calculate the third quartile (Q3):
The median of the upper half of the data set.
In this case, the upper half is: 37, 41, 44, 68, 82.
Q3 = median of the upper half = (44 + 68) / 2 = 56.
Calculate the interquartile range (IQR):
IQR = Q3 - Q1 = 56 - 24.5 = 31.5.
Identify any potential outliers:
According to the boxplot convention, values less than Q1 - 1.5 * IQR or greater than Q3 + 1.5 * IQR are considered potential outliers.
Q1 - 1.5 * IQR = 24.5 - 1.5 * 31.5 = -22.75.
Q3 + 1.5 * IQR = 56 + 1.5 * 31.5 = 103.25.
Analyzing the values in the sample:
None of the values in the sample fall below Q1 - 1.5 * IQR (-22.75) or above Q3 + 1.5 * IQR (103.25).
Therefore, none of the values in the sample will be labeled as outliers.
In summary, none of the values in the given sample (37, 82, 24, 25, 31, 10, 41, 44, 4, 36, 68) will be labeled as outliers in the boxplot.
