Question

54, 76, 80, 75, 69, 86, 76, 65, 59, 78, 56, 82, 77, 78, 83, 65, 97, 93, 91, 33, 73, 57, 95, 85, 77, 58, 89, 80
use salt
(a) create a five - number summary. use rstudio or other software.
lowest value
lowest quartile
median
highest quartile
highest value
(b) create a boxplot.
(c) the test score of 33 should have been identified as an outlier. which of the three reasons for outliers do you think explains this outlier?
a mistake was made when recording the measurement or a question was misunderstood.
the outlier is a legitimate data value and represents natural variation in responses.
the individual(s) in question belong(s) to a different group than the rest of the individuals.
should the outlier be removed when a description of the test scores is presented? explain your reasoning.
yes, it should be removed because it was unduly reported erroneously.
yes, it should be removed because the individual with this test score was probably in the wrong class by accident.
yes, it should be removed because the individual with this test score was probably in the wrong class by accident.
no, it should not be removed because that would cause the natural variability in test scores to be underestimated.
no, it should not be removed because that would cause the natural variability in test scores to be overestimated.

Explanation:

Step1: Sort the data

First, sort the given data set: 33, 54, 57, 58, 58, 59, 63, 65, 65, 66, 69, 70, 72, 73, 75, 75, 76, 76, 77, 77, 78, 78, 80, 80, 81, 82, 83, 85, 85, 87, 89, 91, 92, 93, 95.

Step2: Find the lowest value

The lowest value in the sorted data set is 33.

Step3: Calculate the position of the first - quartile (Q1)

The position of Q1 is $0.25\times(n + 1)$, where $n=35$. So, $0.25\times(35 + 1)=9$. The 9th value in the sorted data set is 65.

Step4: Calculate the position of the median (Q2)

The position of the median is $0.5\times(n + 1)=0.5\times(35 + 1)=18$. The 18th value in the sorted data set is 76.

Step5: Calculate the position of the third - quartile (Q3)

The position of Q3 is $0.75\times(n + 1)=0.75\times(35 + 1)=27$. The 27th value in the sorted data set is 83.

Step6: Find the highest value

The highest value in the sorted data set is 95.

Answer:

Lowest Value: 33
Lowest quartile: 65
Median: 76
Highest quartile: 83
Highest value: 95