\({\bf (1)}\) For each statistic, denote whether it is resistant or not resistant to outliers:
  1. sample mean \(\bar{x}\) not resistant
  2. median resistant
  3. quartiles \(Q1, Q3\) resistant
  4. range not resistant
  5. interquartile range (IQR) resistant
  6. variance not resistant
  7. standard deviation not resistant

\({\bf (2)}\)

A survey of college students in Georgia asked the following questions:
  1. Are you male or female? (recorded as male = 0, female = 1)
  2. What is you height in inches?
  3. Do you routinely smoke cigarettes? (recorded as no = 0, yes = 1)
  4. How many hours do you spend studying?

The figure below shows histograms of the student responses to each of these questions in scrambled order and without scale markings. Which histogram goes with each variable? Explain your reasoning.





\({\bf (3)}\) Consider the following 10 observations of measurements made on Egyptian skulls from five epochs. Use this data to answer parts (a) - (d).

epoch mb bh bl nh
c1850BC 133 131 96 49
cAD150 134 124 91 55
c200BC 141 130 87 49
c200BC 141 131 97 53
c200BC 131 142 95 53
cAD150 141 136 101 54
c4000BC 132 136 100 50
cAD150 130 134 92 52
cAD150 140 135 103 48
cAD150 132 132 99 55
  1. What type of variable is “Epoch”? Qualitative ordinal
  2. Fill in the frequency table below for the variable “Epoch”
    3. names(cts) Frequency
    c4000BC 1
    c1850BC 1
    c200BC 3
    cAD150 5
  3. Use the frequency table from part a.) to construct a bar plot of the variable “Epoch”

  4. What proportion of the observations in the sample are from the epoch “c150AD”? \(\hat{p}_{c150AD} = 0.5\)




\({\bf (4)}\) Again, consider the 10 observations of measurements made on Egyptian skulls from five epochs given in problem \(\bf (1)\). Answer parts (a) - (c)
  1. Construct a histogram for the variable \(nh\) (nasal height) using the following intervals: \(48 < X \leq 50\), \(50< X \leq 52\), \(52< X\leq 54\), and \(54< X\leq 56\). Start by filling in the frequency table below
    2. Interval Frequency
    \(48 < X \leq 50\) 4
    \(50< X \leq 52\) 1
    \(52< X \leq 54\) 3
    \(54< X \leq 56\) 2
  2. Using the histogram above, what proportion of the skulls have a nasal height less than or equal to 54 milimeters? \(\hat{p} = \frac{4+1+3}{10} = 0.8\)
  3. Describe the shape of the distribution above: asymmetric, bimodal





\({\bf (5)}\)

Consider the following \(15\) observations from an experiment on the growth of orange trees. Note that the age in years has been rounded to the nearest \(1/2\)
Age (years) Circumference (mm)
1 0.5 30
2 1.5 51
3 1.5 49
4 2.0 112
5 2.0 75
6 3.0 115
7 3.0 167
8 3.0 125
9 3.5 142
10 4.0 142
11 4.0 174
12 4.0 203
13 4.5 140
14 4.5 203
15 4.5 145
  1. What type of variable is “Age”? quantitative continuous
  2. What type of variable is “Circumference”? quantitative discrete
  3. Give the 5 number summary for the variable “Age”: \(\min = 0.5\), \(Q1 = 2.0\), median \((Q2) = 3\), \(Q3 = 4\), \(\max = 4.5\)
  4. Construct a boxplot using the five number summary above, be sure to make note of any outliers there are no outliers





\({\bf (6)}\)

Consider the following frequency table for the magnitude of earthquakes recorded near the island nation of Fiji.
Magnitude Frequency Relative Frequency Cumulative Relative Frequency
4 191 0.191 0.191
4.5 492 0.492 0.683
5 238 0.238 0.921
5.5 72 0.072 0.993
6 6 0.006 0.999
6.5 1 0.001 1
Total 1000 1 1
  1. Complete the frequency table above
  2. Confirm that the mean magnitude of an earthquake is about \(4.6\) \[\frac{4 \times (191)+4.5 \times (492)+5 \times (238)+5.5 \times (72)+6 \times (6)+6.5 \times (1)}{1000} = 4.6\] or \[4 \times ( 0.191)+4.5 \times ( 0.492)+5 \times ( 0.238)+5.5 \times ( 0.072)+6 \times ( 0.006)+6.5 \times ( 0.001) = 4.6\]
  3. Plot the cumulative distribution of earthquake magnitude
  4. Using the plot above, what is the 75th percentile of the earthquake magnitude? \(Q3 = 5\)