Sets with Highest Variability and Calculating Range and Standard Deviation

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Discussion Assignment #5
1) For each of the data sets below, which appears to have the highest variability? Explain your answer.
a. 3, 3, 4, 4, 4, 2, 3
b. 1, 1, 1, 1, 1, 2, 2, 7
c. 4, 2, 3, 2, 3, 5, 7, 7, 7, 4, 7, 2, 7, 7, 3
2) For each of the data sets above (a,b,c), calculate the range and sample standard deviation.
3) Explain why we need to square the deviations from the mean in our calculation of the standard deviation.

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Discussion Five
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Discussion Five
The data set with the highest variability is the second data set; 1, 1, 1, 1, 1, 2, 2, 7. The degree to which data points differ from one another and from the distribution's mean value is referred to as the variable's variability. Measures of variability, in addition to giving information on the central tendency of the data, also give descriptive statistics that characterize the data. [Case in point:] [Case in point:] [Case in There are a number of different names for variation, including spread, scatter, and dispersion. All of these terms refer to the same concept. Therefore, this data set has the greatest amount of variability since the highest value is seven and the lowest value is one.
Range of data set a) 4-2= 2; thus, the range is 2
Range of data set b) 7-1=6; thus, the range is 6
Range of data set c) 7-2=5; thus, the range is 5
The standard deviation of data set a) 3, 3, 4, 4, 4, 2, 3
s=∑ni=1(xi−x¯¯¯)2n−1
√s=∑i=1n(xi−x¯)2n−1
s=SSn−...

Updated on January 26, 2024

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