webwork / stat-330-001-002 sp18 / hw 01 chapter 1/13 HW 01 chapter 1: Problem 13

Question

webwork / stat-330-001-002 sp18 / hw 01 chapter 1/13 HW 01 chapter 1: Problem 13 Previous Problem List Next (1 point) A sample of 12 measurements has a mean of 36 and a standard deviation of 35 Suppose that the sample is enlarged to 14 measurements, by inckading two additional measurements having a common value of 36 each. A Find the mean of the sample of 14 measurements Mean = B Find the standard deviation of the sample of 14 measurements Standard Deviation- Note: You can eam partial credit on this problem. Preview My Answers Submit Answers You have attempted this problem 0 times You have unlimited attempts remaining. Email instructor 30-001-002-4818/HW.01 chapter 1/13/

Explanation / Answer

Mean is average of values = total addition / count

Here, count =12 and mean = 36

Thus total addition = 36*12 = 432

If we take 2 of 36 each, count = 14 and total addition = 432 + 2*36 = 504

Mean = 504/14 = 36

Standard deviation is square root of variance whereas variance is deviation from mean value

For ex, consider data 2,6,4

Thus mean = 12/3 = 4

Variance = [(2-4)^2 + (4-4)^2 + (6-4)^2] = (4 + 0 +4)/3 = 8/3

If we include 4,4 in this

Mean = 20/5 =4

Variance = [(2-4)^2 + (4-4)^2 + (6-4)^2 + ( 4-4)^2 + (4-4)^2]/5

= 8/5

Thus, numerator won’t change(as added new sample value = mean. Thus, difference =0)

Given: std deviation =3.5

Thus, variance = (3.5)^2

Thus, new variance = (3.5)^2 * 12/14 {due to increase in number of samples}

Thus, new std deviation = sqrt((3.5)^2*12/14)

= 3.24

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