Higher Statistics – Homework 1
US Election Special
(written Tue 8th November 2016)
This homework covers:
Types of data, Frequency table, Bar chart, Stem and leaf, Histogram, Box plot, Outlier, Mean,
Median, Interquartile Range, Standard Deviation
1. Look at the data below, about the US election
(a)
(b)
(c)
(d)
Is each voter’s choice of candidate qualitative or quantitative data?
Is the number of polls that favour Clinton quantitative continuous or quantitative discrete?
Is the average percentage chosing Clinton quantitative continuous or quantitative discrete?
All the polls asked the same question (“Who will you vote for?”) but they didn’t all get the
same result. Speculate why this might be.
(e) Which poll do you think is the most accurate? Give a reason why.
2. For the last ten US elections this has been the turnout, in percent (most recent first):
55, 57, 56, 50, 49, 55, 50, 53, 53, 54
(a) Calculate the mean, median and mode percentage turnout
(b) Calculate the standard deviation
(c) What would the percentage turnout need to be in this year’s election for you to consider it
unusually high, or unusually low?
Higher Statistics 2016/17
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Dr.Hamilton (HSOG)
3. The table below shows the age on becoming president
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
(a)
(b)
(c)
(d)
(e)
George Washington
John Adams
Thomas Jefferson
James Madison
James Monroe
John Quincy Adams
Andrew Jackson
Martin Van Buren
William Harrison
John Tyler
James Polk
Zachary Taylor
Millard Fillmore
Franklin Pierce
James Buchanan
Abraham Lincoln
Andrew Johnson
Ulyssses S Grant
Rutherford Hayes
James Garfield
Chester Arthur
Grover Cleveland
Benjamin Harrison
Grover Cleveland
William McKinley
Theodore Roosevelt
William Taft
Woodrow Wilson
Warren Harding
Calvin Coolidge
Herbert Hoover
Franklin Roosevelt
Harry Truman
Dwight Eisenhower
John F Kennedy
Lyndon Johnson
Richard Nixon
Gerald Ford
Jimmy Carter
Ronald Reagan
George Bush Senior
Bill Clinton
George W Bush
Barack Obama
Years President
1789-1797
1797-1801
1801-1809
1809-1817
1817-1825
1825-1829
1829-1837
1837-1841
1841-1841
1841-1845
1845-1849
1849-1850
1850-1853
1853-1857
1857-1861
1861-1865
1865-1869
1869-1877
1877-1881
1881-1881
1881-1885
1885-1889
1889-1893
1893-1897
1897-1901
1901-1909
1909-1913
1913-1921
1921-1923
1923-1929
1929-1933
1933-1945
1945-1953
1953-1961
1961-1963
1963-1969
1969-1974
1974-1977
1977-1981
1981-1989
1989-1993
1993-2001
2001-2009
2009-
Age on becoming president
57
61
57
57
58
59
61
58
68
51
49
64
50
48
65
52
56
46
54
49
51
55
55
63
54
42
51
56
65
50
54
51
60
62
43
55
56
60
55
59
64
46
54
48
Plot the Age on Becoming President in a Steam and Leaf diagram
Grouping the ages in 10s, plot the Age on Becoming President in a histogram
Find the mean, median and mode Age on Becoming President
Find the upper and lower quartiles, and the semi-interquartile range
Make a box and whisker plot of the Age on Becoming President
Higher Statistics 2016/17
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Dr.Hamilton (HSOG)
(f) Suppose Donald Trump’s team found that Barack Obama was actually just 28 on
becoming president (thus being ineligible, as the minimum age is 35).
Without doing any calculation, how would this affect the mean, median and mode Age
on Becoming President
4. The map below shows the number of Electoral College votes each state has.
A presidential candidate needs to win 270 votes to win the election.
(a) State the minimum and maximum votes per state
(b) By looking at the data alone, which states could be considered outliers?
5. Donald Trump’s catchphrase is “Make America Great Again”
The number of times he says this each day is normally distributed with a mean of 20 and a
variance of 25
(a)
(b)
(c)
(d)
What is the standard deviation?
What is the likelihood of him saying it 30 or more times?
What is the likelihood of him saying it 20 or less times?
Sketch a graph showing this distribution
Optional extra question
6. Can you trust poll results?
(a) Read http://www.quickanddirtytips.com/education/math/how-to-use-statistics-tounderstand-poll-results
(b) Summarise what it says, in one short paragraph
Higher Statistics 2016/17
3
Dr.Hamilton (HSOG)