Transcript Answers - The Joy of Stats

First Quiz Answers
Graduate Stats Course
Question 1: Answers [1]
1.1 TYPE OF ANIMAL is nominal. Once we make
this choice, we cannot obtain the mean,
median, or standard deviation.
TYPE OF ANIMAL is like EYE COLOUR in the
class data file.
1.2 Frequency table: The relative frequency of
monkeys is 25/115 = 22%.
Question 1: Answers [2]
1.3
Mode is dog. (When a variable is at the
nominal level, the mode is a category name.)
1.4 Modal frequency is 60 (OK: 52%).
1.5 to 1.9 Answers should be X; these measures
cannot be obtained for nominal-level
variables.
1.10 Total number of animals = 115.
Question 1: Last Comment
The question states that TYPE OF ANIMAL is a
variable defined on animals — individual animals
(not species or groups of animals) are the cases.
Question 2: Answers [1]
2.1 Total revenue = $19,350.
2.2 to 2.3 Mean price of the 115 animals
= 19,350/115.
The answer is $168.26.
Total revenue goes in the numerator, and the
total number of cases (individual animals) in
the denominator.
Question 2: Answers [2]
2.4 The median price is $100 dollars. All animals
— all 115 of them — parade by, each one
carrying its price tag. We find the middle
animal in the parade — the one at the 58th
position — and its price is the median price.
(The animal happens to be a dog.)
Question 2: Answers [3]
2.5 Jay-Jay Diamond is a snake: Yes, we can find
her price Z-score (PRICE is an interval-ratio
variable, so, for each case/animal, there is a
number for the value of the variable). This is
like finding the Z-scores for each case/person
in the class for HEIGHT.
Her price — $20 — is below the mean of
$168.26, so the Z-score is negative.
2.6 The Z-score numerator is (20 – 168.26).
Question 3: The Survey [1]
This question relates to a new data file, which
contains the results of a survey.
New cases = the respondents.
3.1 NAME PREFERENCE is a nominal-level
variable; named categories, no order.
3.2 Therefore, the bar chart, pie chart, and
frequency table are ways to display the
distribution. (The others require interval-ratio
data.)
3.3 6/41 = 14.6% preferred The Pet-o-phile.
Question 3: Answers [2]
3.4 The new variable WEIRD OR NORMAL is a
binary or dichotomous variable.
3.5 The mean of the variable is the proportion of
cases with a code 1 for that variable —
i.e., proportion answering with weird name
choices. This proportion is p.
Mean = (21 + 0)/41 = .51
3.6 The variance is (p)(1 – p) = .2499 or .25
Question 4: Answers
4.1 They have computed measures of central
tendency (mean, median, and mode).
4.2 They have failed to examine VARIABILITY in
the distribution. (Measures of variability can
include variance, standard deviation, and an
examination of percentile spread as in a
boxplot.) The general concept is
VARIABILILTY, DISPERSION, SPREAD or
even just DIFFERENCE (or disparities,
inequalities, and other synonyms).
Questions 5 and 6
5
Memorize the formula once you have thought
about the algorithm. In the denominator, you
can put N for a population or N – 1 for a
sample.
6
Choices of statistics have political implications.
Here, using only the mean would be very
deceptive. There are major inequalities in the
pay scale of this factory. (Using the midpoint of
the interval is OK, though.)
Thinking about Stats
Bring together
 A term (vocabulary): E.g., standard deviation
 The broader concept: Variability of a distribution
 The formula and its algorithm
 The appropriate application — a “story problem”
context