Mrs. Keegan wrote down her student's quiz grades from Unit 2. Their results included: 58, 72, 88, 100, 65, 93, 81. Which number, if added to the dataset, would represent an outlier in the data?
To identify an outlier in the data, we can use the concept of the interquartile range (IQR).
First, we need to find the first quartile (Q1) and the third quartile (Q3) of the dataset. To do this, we arrange the numbers in ascending order: 58, 65, 72, 81, 88, 93, 100.
Q1 is the median of the lower half of the dataset, which is the median of {58, 65, 72}. The median of this set is the number in the middle, so Q1 = 65.
Q3 is the median of the upper half of the dataset, which is the median of {81, 88, 93, 100}. The median of this set is the number in the middle, so Q3 = 88.
Next, we can calculate the IQR: IQR = Q3 - Q1 = 88 - 65 = 23.
According to the IQR rule, any data point that is less than Q1 - 1.5 * IQR or greater than Q3 + 1.5 * IQR is considered an outlier.
Q1 - 1.5 * IQR = 65 - 1.5 * 23 = 65 - 34.5 = 30.5.
Q3 + 1.5 * IQR = 88 + 1.5 * 23 = 88 + 34.5 = 122.5.
Given the dataset of quiz grades, the number 100 is the only one that falls within the range of a potential outlier. Therefore, 100 would represent an outlier in the data.