UI STAT 251 Spring 2011
Quiz 1
UI#:
NAME:
1. (1 points) For a right skewed distribution, the mean and median are not equal. Which one is
generally larger? Why?
Mean>median, there are some large values that make the mean larger, but they influence the
median a little.
2. (1 points) “There are 55% of the data observations lies inside the Interquartile range of a data set.”
True or False.
False
3. (1 points) Find the median of the data set {5, 3, 7, 6, 2, 8, 70, -1, -2}.
> x=c(5, 3, 7, 6, 2, 8, 70, -1, -2)
> median(x)
[1] 5
4. (2 points) Numerically compute the standard deviation of the data set {7, 3, 5, 1}. You can do this
by hand or by the software R.
> x=c(7, 3, 5, 1)
> sd(x)
[1] 2.581989
5. (2 points) Which data set has a larger standard deviation (without computing them out):
set 1 = { 6, 9, 10, 17, 18, 22, 25}, or
set 2 = { 8, 9, 10, 17, 18, 22, 23}. Explain your answer in a brief statement.
The means of these two data sets are the same. But in set 1, it has 6 and 25 which are more far away
from the mean than set 2, which has 8 and 23. The rests of the data are the same. So set 1 has larger
standard deviation.
6. (3 points) Open up the software R in your laptop. Type faithful$eruptions to retrieve the
old faithful eruptions data set. Find the mean, standard deviation, and the 37-percentile of this
eruptions data set.
> mean(faithful$eruptions)
[1] 3.487783
> sd(faithful$eruptions)
[1] 1.141371
> quantile(faithful$eruptions,.37)
37%
3.34218