What is the point estimate for the average number of credits taken per semester by students at this college? What about the median?

mean(credits[,1])
## [1] 13.65
median(credits[,1])
## [1] 14
hist(credits[,1],col="sky blue",xlab="",,ylab="",main="College Credits")

What is the point estimate for the standard deviation of the number of credits taken per semester by students at this college? What about the IQR?

IQR = 3rd quartile - 1st quartile

summary(credits[,1])
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    8.00   13.00   14.00   13.65   15.00   18.00
IQR(credits[,1])
## [1] 2

Is a load of 16 credits unusually high for this college? What about 18 credits? Explain your reasoning.

lower_limit = mean(credits[,1]) - 2*sd(credits[,1])
upper_limit = mean(credits[,1]) + 2*sd(credits[,1])
print(lower_limit)
## [1] 9.832179
print(upper_limit)
## [1] 17.46782

16 is within 2sd of the mean, so it is not unusual; but 18 is because it falls outside of this range.

The college counselor takes another random sample of 100 stduents and this time finds a sample mean of 14.02 units. Should she be surprised that this sample statistic is slightly different than the one from the original sample?

Not at all, because these are point estimates based on samples and there isn’t much difference between 14.02 and 13.65.

The sample means given above are point estimates for the mean number of credits taken by all students at that college. What measures do we use to quantify the variability of this estimate? Compute this quantity using the data.

The standard error is used which is sigma/sqrt(n).

sd(credits[,1])/sqrt(nrow(credits))
## [1] 0.1908911