The final exam scores listed below are from one section of MATH 200. How many scores were within one standard deviation of the mean? How many scores were within two standard deviations of the mean?
99 34 86 57 73 85 91 93 46 96 88 79 68 85 89
First, calculate the mean: 99+34+86+57+73+85+91+93+46+96+88+79+68+85+89 divided by 15 1169/15 = 77.93 or 78
Next, find the range: Highest minus lowest 99-34 = 65
Find the variance: (99-78) ²+(34-78) ²+(86-78) ²+(57-78) ²+(73-78) ²+(85-78) ²+(91-78) ²+(93-78) ²+(46-78) ²+(96-78) ²+(88-78) ²+(79-78) ²+(68-78) ²+(85-78) ²+(89-78) ² divided by 15
(21) ²+(-44) ²+(8) ²+(-21) ²+(-5) ²+(7) ²+(13) ²+(15) ²+(-32) ²+(18) ²+(10) ²+(1) ²+(-10) ²+(7) ²+(11) ² divided by 15
441+1936+64+441+25+49+169+225+1024+324+100+1+100+49+121/15
5069/15 = 337.9 or 338 variance
Square the variance to get the standard deviation: sq rt 338 = 18.38 (18 rounded)
Mean – standard deviation: 78+18= 96
Mean + standard deviation: 78-18= 60
Standard Deviation = 60 to 96 (11 scores fall in this category) (4 scores do not fall in between those numbers)
Mean plus one standard deviation: 78 + 18 = 96
Mean plus two standard deviations: 78 + 18(2) 78 + 36 = 114 (96 to 114)
I don't know how to answer those two questions based on my calculations... Did i do this equation correctly?