Question

# An analyst produced the following summary statistics describing a quantitative variable: n Mean Variance Std. dev. Median Range Q1 Q3 108 79.9 64.63 8

Describing quantitative data
An analyst produced the following summary statistics describing a quantitative variable:
n Mean Variance Std. dev. Median Range Q1 Q3
108 79.9 64.63 8.04 79.05 44.7 74 85.4
(a) The smallest value in the data set is 51. Should the analyst consider the value 51 to be an outlier on the low side?
(b) Justify your answer using an appropriate outlier identification rule. If you perform a calculations, give the pertinent calculations. If you create a graph, copy and paste it into the space.

2020-12-06

Step 1
Given summary statistics as,
n Mean Variance Std. dev. Median Range Q1 Q3
108 79.9 64.63 8.04 79.05 44.7 74 85.4
Step 2
a) An outlier is a value that is much larger or smaller than the other values in a data set, or a value that lies outside the given data set.
Yes, the lowest value can be an outlier, analyst can consider it as an outlier if it lies outside the lower fence $$Q1 -1.5 \cdot IQR$$
b) Outlier identification rule: The data point is said to be an outlier if it is lower than (lower quartile - $$1.5 \cdot IQR$$) or more than (upper quartile $$+ 1.5 \cdot IQR$$)
We can check 51 is an outlier or not using above rule.
51 is lower value.
And lower quartile $$(Q1) = 74$$
And inter quartile range $$(IQR) = Q3 - Q1$$
$$= 85.4 - 74$$
$$= 11.4$$
Hence lower fence $$= Q1 - 1.5 \cdot IQR$$
$$= 74 - 1.5 \cdot 11.4$$
$$= 56.9$$
Since 51 is lower than 56.9 so that we can say 51 is an outlier.