The time, in minutes, it took each of 11 students to complete a puzzle was recorded and is shown in the following list.
9, 17, 20, 21, 27, 29, 30, 31, 32, 35, 58
One of the students who completed the puzzle claimed that there were two outliers in the data set. Based on the 1.5×IQR
rule for outliers, is there evidence to support the student’s claim?
Yes, there are two outliers. One outlier is 9 minutes and the other outlier is 58 minutes.
A
No, there is only one outlier at 9 minutes.
B
No, there is only one outlier at 58 minutes.
C
No, there are three outliers. One outlier is 9 minutes, one outlier is 35 minutes, and one outlier is 58 minutes.
D
No, there are no outliers.
E
C? outlier 58 minutes
The Answer is C). No, there is only one outlier at 58 minutes.
BECAUSE...
9, 17, 20, 27, 29, 30, 31, 32, 35, 58
Q1... 20
Median... 29
Q3... 32
IQR... Q3-Q1... 32-20... 12
Outlier Rule... Q1-(1.5)(IQR) & Q3+(1.5)(IQR)
(1.5)(IQR)... (1.5)(12)= 18
20-18= 2
32+18= 50
Outliers are any numbers lower than 2 and more than 50!
:)
No, there are no outliers. The outlier rule considers values that fall beyond 1.5 times the interquartile range (IQR) as outliers. In this case, the IQR is calculated as the difference between the third quartile (Q3) and the first quartile (Q1).
Q1 = 21 minutes
Q3 = 31 minutes
IQR = Q3 - Q1 = 31 - 21 = 10 minutes
According to the 1.5×IQR rule, any value less than Q1 - 1.5×IQR or greater than Q3 + 1.5×IQR would be considered an outlier. In this case, the range for potential outliers would be:
Q1 - 1.5×IQR = 21 - 1.5 × 10 = 21 - 15 = 6 minutes
Q3 + 1.5×IQR = 31 + 1.5 × 10 = 31 + 15 = 46 minutes
Since no values in the list fall outside the range of potential outliers, there is no evidence to support the claim that there are outliers. The correct answer is E: No, there are no outliers.
To determine if there are any outliers in the data set, we can use the 1.5×IQR rule. First, we need to find the IQR (interquartile range), which is the difference between the third quartile (Q3) and the first quartile (Q1) of the data set.
To calculate Q1 and Q3, we need to find the median of the first half of the data (lower half) and the median of the second half of the data (upper half) respectively.
First, let's arrange the data in ascending order:
9, 17, 20, 21, 27, 29, 30, 31, 32, 35, 58
Counting the number of observations, we see that we have an odd number of data points (11). The median (Q2) will be the value in the middle, which is the 6th value in this case: 29.
Next, we find Q1, which is the median of the lower half of the data set. Counting from the beginning, we have 5 values in the lower half. The median is the middle value, which is the 3rd value: 20.
Similarly, we find Q3, which is the median of the upper half of the data set. Counting from the end, we have 5 values in the upper half. The median is the middle value, which is the 3rd value from the end: 32.
Now we can calculate the IQR:
IQR = Q3 - Q1 = 32 - 20 = 12
According to the 1.5×IQR rule, any values below Q1 - 1.5×IQR or above Q3 + 1.5×IQR can be considered as outliers.
Q1 - 1.5×IQR = 20 - 1.5×12 = 2
Q3 + 1.5×IQR = 32 + 1.5×12 = 50
Looking at the data set, we see that there is only one value below 2 (9 minutes) and one value above 50 (58 minutes). Therefore, we can conclude that there are two outliers in the data set.
The correct answer is C: No, there is only one outlier at 58 minutes.