Concept explainers
The following set of data is from a sample of n = 5:
7 4 9 8 2
- Calculate the
mean ,median , andmode . - Calculate the
range , variance. standard deviation, and coefficient of variation. - Calculate the Z scores. Are there any outliers?
- Describe the shape of the data set.
(a)
To compute: The mean, median, and mode for the given data set.
Answer to Problem 3.1LB
Mean is 6, median is 7 for the given dataset.
Explanation of Solution
Given:
Given data set is:
7,4,9,8, and 2.
Formula:
Calculation:
Mean could be calculated as for the given data set:
Median could be calculated as for the given data set:
Arrange the data in ascending ordered:
2,4,7,8, and 9.
Thus, Median is 7.
Mode:
There is no mode.
(b)
To conclude:
The range, variance, standard deviation, and coefficient of variation.
Answer to Problem 3.1LB
The is 7, variance is 11.33, standard deviation is 3.366 for the given data set.
Explanation of Solution
Given:
From the above given data set,
Calculation:
The range could be calculated as:
Formula:
The standard deviation
The standard deviation
(c)
To compute:
The Z-score, there is any outliers.
Answer to Problem 3.1LB
z scores are -1.18, -0.29, 0.89, -0.59, 0.59.
Explanation of Solution
Given:
from the above part,
Formula:
Calculation:
Z score can be calculated:
x =2,7,9,4,8
Thus,
Thus,
Z =-1.18, -0.29,0.89,-0.59,0.59
There is one value outlier 2 because 2 does not lie in the interval
(d)
To explain:
The shape of the data set.
Explanation of Solution
Given:
from the above given data set:
Graph:
The graph could be construct for the given data set as:
Interpretation:
Shape:
It seems that there would be two nods.
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