2.69 a, c 2 1 1 1 1 3 2 6 1 1 2 1 1...

2.69 a, c

2	1	1	1
1	3	2	6
1	1	2	1
1	3	2	1
1	2	1	3
4	3	2	5
4	2	2	2
1	1

Refer to the data set above, with 30 values.

Find the range, variance, and standard deviation of this data set.

Eliminate the smallest and largest value from the data set and repeat part a. What effect does dropping both of these measurements have on the measures of variation found in part a.?

Expert Solution

1)

	Xi	(Xi-Xbar)^2
	2	0.0000
	1	1.0000
	1	1.0000
	1	1.0000
	1	1.0000
	4	4.0000
	4	4.0000
	1	1.0000
	1	1.0000
	3	1.0000
	1	1.0000
	3	1.0000
	2	0.0000
	3	1.0000
	2	0.0000
	1	1.0000
	1	1.0000
	2	0.0000
	2	0.0000
	2	0.0000
	1	1.0000
	2	0.0000
	2	0.0000
	1	1.0000
	6	16.0000
	1	1.0000
	1	1.0000
	3	1.0000
	5	9.0000
	2	0.0000
sum	60.0	50.0000
sum/n	2
sum/(n-1)		1.7241

mean = sum(Xi)/n = 2.00

VARIANCE = sum(Xi-Xbar)^2/(n-1) = 1.7241

Sd = sqrt { (Xi-Xbar)^2/(n-1) }
sqrt(1.72414) = 1.31

range = max - min = 6-1 = 5

2) if the minimum and maximum values are dropped, the mean will be affected as it considers each observation in the data. the variance and standard deviation will be also be affected. the range is the difference between the maximun and minimum value, hence it will also be affected.

	Xi	(Xi-Xbar)^2
	2	0.0115

	1	0.7972
	1	0.7972
	1	0.7972
	4	4.4401
	4	4.4401
	1	0.7972
	1	0.7972
	3	1.2258
	1	0.7972
	3	1.2258
	2	0.0115
	3	1.2258
	2	0.0115
	1	0.7972
	1	0.7972
	2	0.0115
	2	0.0115
	2	0.0115
	1	0.7972
	2	0.0115
	2	0.0115
	1	0.7972

	1	0.7972
	1	0.7972
	3	1.2258
	5	9.6543
	2	0.0115
sum	53.0	33.0957
sum/n	1.892857
sum/(n-1)		1.2258

mean = sum(Xi)/n = 1.89
VARIANCE = sum(Xi-Xbar)^2/(n-1) = 1.2258

Sd = sqrt { (Xi-Xbar)^2/(n-1) }
sqrt(1.22576530612245)
1.11

range = max - min = 5-1 = 4

orchestra answered 1 year ago

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