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
To identify an outlier in a dataset, we need to understand the concept of outliers. An outlier is a data point that significantly deviates from other observations in a dataset.
There are different ways to identify outliers. One common method is using the IQR (Interquartile Range) method, which involves calculating the range between the first quartile (Q1) and the third quartile (Q3). Any value that lies more than 1.5 times the IQR above Q3 or below Q1 is considered an outlier.
Let's calculate the IQR for the given dataset, which includes the quiz grades from Unit 2: 58, 72, 88, 100, 65, 93, 81.
Step 1: Arrange the dataset in ascending order:
58, 65, 72, 81, 88, 93, 100.
Step 2: Calculate the first quartile (Q1) and the third quartile (Q3):
Q1 = (65 + 72) / 2 = 68.5
Q3 = (88 + 93) / 2 = 90.5
Step 3: Calculate the IQR:
IQR = Q3 - Q1 = 90.5 - 68.5 = 22
To identify an outlier, we need to check if any value is more than 1.5 times the IQR above Q3 or below Q1.
1. Option A: 53
Since 53 is less than Q1, it is not an outlier.
2. Option B: 99
Since 99 is more than 1.5 times the IQR above Q3 (90.5 + 1.5 * 22 = 124), it is a potential outlier.
3. Option C: 35
Since 35 is less than Q1, it is not an outlier.
4. Option D: 69
Since 69 is between Q1 and Q3, it is not an outlier.
Based on the calculations above, the value that represents a potential outlier in the dataset is 99, which corresponds to Option B.
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.