Question

In: Statistics and Probability

For the following data 86 84 91 75 78 80 74 75 87 76 82 90...

For the following data

86 84 91 75 78 80 74 75 87 76 82 90 98 68

What is the mean? ______

What is the median?_________

What is the mode (if any)? _____

What is the standard deviation? ____

What is the variance? ______

What is the five-number summary for this data?

Draw a boxplot with reasonable attention to scale.

Create a stemplot of this data.

Using the same data set and ignoring the fact that the 5-number summary would change a bit, what number would be add to the lower end of this data that would be an outlier?

What number did you add? ______

How did you determine that your choice of this new value? Use correct terminology. (Hint: IQR)
If you selected one number randomly from the original data, what is the likely hood that it would be an even number or greater than 85?(Show the equation you used to find this answer or explain your thought process.)

Expert Solution

mean = ΣX/n = 1144.000 / 14 = 81.7143

Median=0.5(n+1)th value = 7.5th value of sorted data
= 81.000

mode= highest frequency data = 75

sample variance =    Σ(X - X̄)²/(n-1)=   858.8571   /   13   =   66.066

sample std dev =   √ [ Σ(X - X̄)²/(n-1)] =   √   (858.8571/13)   =       8.1281

-------------------------

maximum = 98
minimum= 68

Median=0.5(n+1)th value =    7.5th   value of sorted data
=   81.000

quartile , Q1 = 0.25(n+1)th value=   3.75th   value of sorted data
=   75

Quartile , Q3 = 0.75(n+1)th value=   11.25th   value of sorted data
=   87.75

-------------------------------------

Frequency	Stem	Leaf
1	6	8
5	7	4 5 5 6 8
5	8	0 2 4 6 7
3	9	0 1 8
14

68 will be lowest number

thanks

revert back for doubt

please upvote

orchestra answered 2 years ago

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