Respuesta :
Answer:
Mean=2891.125.
Standard deviation=623.3918
Step-by-step explanation:
Let X be the birth weights of SIDS cases in King County, Washington.
The appropriate last observation is 2863.(also confirmed by web search)
Sample mean=xbar=sumx/n
sumx=2466 +3941 +2807 +3118 +2098 +3175 +3515 +3317 +3742 +3062 +3033 +2353 +2013 +3515 +3260 +2892 +1616 +4423 +3572 +2750 +2807 +2807 +3005 +3374 +2722 +2495 +3459 +3374 +1984 +2495 +3062 +3005 +2608 +2353 +4394 +3232 +2013 +2551 +2977 +3118 +2637 +1503 +2438 +2722 +2863 +2013+ 3232 +2863
sumx=138774
Xbar=138774/48
Mean=Xbar=2891.125
X X-Xbar (X-Xbar)²
2466 -425.125 180731.2656
3941 1049.875 1102237.516
2807 -84.125 7077.015625
3118 226.875 51472.26563
2098 -793.125 629047.2656
3175 283.875 80585.01563
3515 623.875 389220.0156
3317 425.875 181369.5156
3742 850.875 723988.2656
3062 170.875 29198.26563
3033 141.875 20128.51563
2353 -538.125 289578.5156
2013 -878.125 771103.5156
3515 623.875 389220.0156
3260 368.875 136068.7656
2892 0.875 0.765625
1616 -1275.125 1625943.766
4423 1531.875 2346641.016
3572 680.875 463590.7656
2750 -141.125 19916.26563
2807 -84.125 7077.015625
2807 -84.125 7077.015625
3005 113.875 12967.51563
3374 482.875 233168.2656
2722 -169.125 28603.26563
2495 -396.125 156915.0156
3459 567.875 322482.0156
3374 482.875 233168.2656
1984 -907.125 822875.7656
2495 -396.125 156915.0156
3062 170.875 29198.26563
3005 113.875 12967.51563
2608 -283.125 80159.76563
2353 -538.125 289578.5156
4394 1502.875 2258633.266
3232 340.875 116195.7656
2013 -878.125 771103.5156
2551 -340.125 115685.0156
2977 85.875 7374.515625
3118 226.875 51472.26563
2637 -254.125 64579.51563
1503 -1388.125 1926891.016
2438 -453.125 205322.2656
2722 -169.125 28603.26563
2863 -28.125 791.015625
2013 -878.125 771103.5156
3232 340.875 116195.7656
2863 -28.125 791.015625
The sample standard deviation can be calculated as
[tex]Standard deviation=\sqrt{\frac{sum(x-xbar)^2}{n-1} }[/tex]
sum(X-Xbar)² =180731.2656 +1102237.516 +7077.015625 +51472.26563 +629047.2656 +80585.01563 +389220.0156 +181369.5156 +723988.2656 +29198.26563 +20128.51563 +289578.5156 +771103.5156 +389220.0156 +136068.7656 +0.765625 +1625943.766 +2346641.016 +463590.7656 +19916.26563 +7077.015625 +7077.015625 +12967.51563 +233168.2656 +28603.26563 +156915.0156 +322482.0156 +233168.2656 +822875.7656 +156915.0156 +29198.26563 +12967.51563 +80159.76563 +289578.5156 +2258633.266 +116195.7656 +771103.5156 +115685.0156 +7374.515625 +51472.26563 +64579.51563 +1926891.016 +205322.2656 +28603.26563 +791.015625 +771103.5156 +116195.7656 +791.015625
sum(X-Xbar)² =18265013.25
[tex]Standard deviation=\sqrt{\frac{18265013.25}{48-1} }[/tex]
[tex]Standard deviation=\sqrt{\frac{18265013.25}{47} }[/tex]
[tex]Standard deviation=\sqrt{388617.3032}[/tex]
Standard deviation=623.3918.
