EJackson Howework 2

Questions

1. Calculate the mean and the standard deviation for the Age variable. M = 19.62, SD = 4.43 (rounded to hundredth)

2. If you add another 18 year old to the sample, what happens with the mean? Why would this happen?

Adding another score (age) of 18 would reduce the mean. As mean is the average of scores, the addition of an 18 year old (which represents the lowest age) would reduce the mean.

3. Determine if females (coded as 0) or males (coded as 1) have a higher mean Score.

Females M = 329.48 (hihger) than Males M = 315.00

4. Determine if Sophomores (coded as 2) or Juniors (coded as 3) have a higher variance on the Score variable.

Sophomores (261.75) had higher variance on scores than Juniors (144.01)

5. What is the standard deviation for the group that was higher in question 4? Sophomore standard deviation is 4.43.

#end of answers

#Hand Calculations

1. steps to calculate mean

#Calculate the sum of the Age Variable

ssum = sum(EJackson_HW2$age)

#Calculate the sample size

n = length(EJackson_HW2$age)

#Calculate the mean

smean = ssum/n

Sum: 569 / Sample size: 30 / Mean: 18.97

#1. steps to calculate standard deviation

#Squared mean differences

smdiff = (EJackson_HW2$age)

#Sum of squares

SS = sum(smdiff)

#Variance

variance = SS/(n-1)

#Results

##Sum of squares: 569 / Variance: 19.6

SD = sqrt(variance)

Standard Deviation: 4.4295

Question 3

#Determine level of measurement of biosex

is.factor(EJackson_HW2$biosex)

#The answer was false, so …

EJackson_HW2\(biosex = factor(EJackson_HW2\)biosex)

#Subset the data

Males = subset(EJackson_HW2, EJackson_HW2$biosex == ‘1’)

Females = subset(EJackson_HW2, EJackson_HW2$biosex == ‘0’)

#Determine mean of females (0)

ssum = sum(Females$score)

n = length(Females$score)

mmean = sum(Females\(score)/length(Females\)score)

#Results for Females

Sum: 5271.69 / Sample size: 16 / Mean: 329.48

#Determine mean of Males (1)

ssum = sum(Males$score)

n = length(Males$score)

mmean = sum(Males\(score)/length(Males\)score)

#Results for Males

Sum: 4409.97 / Sample size: 14 / Mean: 314.99

Question 4

#Subsetting Class Rank

Sophomores = subset(EJackson_HW2, EJackson_HW2$classrnk == ‘2’)

#finding the SD for Sophmores

mmean = sum(Sophomores\(score)/length(Sophomores\)score)

msmdiff = (Sophomores$score - mmean)^2

mSS = sum(msmdiff)

mVariance = mSS/(length(Sophomores$score) - 1)

mSD = sqrt(mVariance)

SD = sqrt(variance)

Standard Deviation for Sophomores is 4.43, variance 261.75

#Subsetting Class Rank

Juniors = subset(EJackson_HW2, EJackson_HW2$classrnk == ‘3’)

#finding the SD for Juniors

mmean = sum(Juniors\(score)/length(Juniors\)score)

msmdiff = (Juniors$score - mmean)^2

mSS = sum(msmdiff)

mVariance = mSS/(length(Juniors$score) - 1)

mSD = sqrt(mVariance)

SD = sqrt(variance)

Standard Deviation for Juniors is 4.43, variance 144.01