Home › CBEST › Mathematics › Descriptive Statistics › A data set has a first quartile of 20 and a thir…
A data set has a first quartile of 20 and a third quartile of 60. A value more than 1.5 interquartile ranges above the third quartile is suspect. What is that cut-off?
A100
B140
C90
D120
Answer & Solution
Correct answer: D. 120
1. First find the interquartile range, which is the third quartile minus the first.
2. That is 60 minus 20, which is 40.
3. Now take 1.5 times that spread.
4. 1.5 multiplied by 40 is 60.
5. Add that to the third quartile: 60 plus 60 is 120.
6. So any value above 120 is a potential outlier.
7. Answering 100 adds one interquartile range instead of one and a half.
8. Answering 90 adds only half of the interquartile range.
_Source: OpenStax High School Statistics (CC BY 4.0), Ch 2 "Descriptive Statistics" and Ch 3 "Probability Topics", section 2.3 Measures of the Location of the Data_
Related questions
When first looking at a graph of data, you should look for an overall pattern and any:Measures of location, as opposed to centre or spread, are quartiles and:Alongside stemplots and box plots, the third standard display for one variable is the:Alongside range and standard deviation, the third standard measure of spread is:The third measure of centre, besides mean and median, is the:Looking at house prices, a better summary than the mean alone is the median together with:Comparing the mean and the median, outliers:When a distribution is skewed to the right, the mean is usually: