Question

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?
A 53
B 99
C 35
D 69

Answer 1

Only 53,99,35, or 69

Answer 2

The dataset in ascending order is: 58, 65, 72, 81, 88, 93, 100.

To determine if a number is an outlier in the data, we can use the interquartile range (IQR) method. First, we need to find the first quartile (Q1) and third quartile (Q3) of the dataset. The IQR is then calculated as Q3 - Q1.

Q1 is the median of the lower half of the data, which is (65 + 72)/2 = 68.5
Q3 is the median of the upper half of the data, which is (88 + 93)/2 = 90.5

The IQR is 90.5 - 68.5 = 22.

To determine if a number is an outlier, we can use the following rule:

- Any number less than Q1 - 1.5 * IQR is considered a mild outlier.
- Any number greater than Q3 + 1.5 * IQR is considered a mild outlier.

Using this rule, we can calculate the boundaries for outliers:

Q1 - 1.5 * IQR = 68.5 - 1.5 * 22 = 68.5 - 33 = 35.5
Q3 + 1.5 * IQR = 90.5 + 1.5 * 22 = 90.5 + 33 = 123.5

Therefore, any number less than 35.5 or greater than 123.5 would be considered an outlier.

To determine which number, when added to the dataset, would represent an outlier, we can check if any of the answer choices fall outside the range of 35.5 and 123.5.

A) 53 is within the range of 35.5 and 123.5
B) 99 is within the range of 35.5 and 123.5
C) 35 is equal to the lower boundary of 35.5
D) 69 is within the range of 35.5 and 123.5

None of the answer choices would represent an outlier if added to the dataset.

Therefore, the answer is none of the above.

Answer 3

In that case, the answer would be B) 99. When added to the dataset, 99 would fall outside the range of the lower and upper boundaries for outliers (35.5 and 123.5), making it an outlier in the data.