Transcript First quiz answers

First Quiz Answers
Undergraduate Stats Course
Thinking about Question 1 [1]
The “trick” to thinking about Question 1 is to be
sure we can identify
 The cases: What are they?
 The variable: What is it, and what cases is it
defined on?
 The values of the variable: What are they?
 The level of measurement
Thinking about Question 1 [2]
It may be helpful to think about an SPSS/PASW
data file and what would be filled in for
 Cases
 Variables
 Values for each variable
Note: TYPE OF ANIMAL is like EYE COLOUR and
MOVIE FAVES in our class data file.
Question 1: Answers [1]
1.1 Nominal. Once we say nominal, there are
some things we can’t do!
We cannot compute a mean, median, variance, or
standard deviation
Relative Frequencies
for Nominal Variables
TYPE OF ANIMAL is a variable defined on the
animals. The cases are animals and the values are
names of animal types (dogs, etc).
1.2 Relative frequency of snakes. We can make a
frequency table; the relative frequency means
a percentage, which is 8.3%. (8.3% of the total
of 120 animals were snakes.)
Note: 8.3% is a lot more than .83%. Be careful!
Question 1: Answers [2]
1.3 Mode (value with the most cases) of the
variable TYPE OF ANIMAL: dogs.
1.4 Modal frequency of dogs: 50.
1.5 Mean of TYPE OF ANIMAL: This is a nominal
variable — we cannot compute a mean,
median, or standard deviation.
1.6 to 1.10 X for all the remaining questions
except the last one; total number of animals
sold = 120.
Question 2: Answers [1]
2.1 Total revenue: $7360.
2.2 Mean price of an animal: $61.33.
2.3 Divide $7360 by 120.
2.4 Median price was $50 — parade all 120
animals, lined up in order of their price tag.
The 60th and 61st cases both have a price tag
of $50 (they happen to be cats).
Question 2: Answers [2]
2.5 Jay-Jay is a snake. Her sale price is $12. This
is well below the mean sale price of $61.33.
Therefore her price Z-score is negative.
2.6 The numerator is (12 – 61.33). We have not
computed the SD yet, which is the value for
the denominator.
Thinking about Question 3
It relates to a new data file of survey results:
 Cases are respondents
 Variable is NAME PREFERENCE
 Values are the specific names
Question 3: Answers
3.1 NAME PREFERENCE is nominal.
3.2 Display its distribution in a bar chart, pie chart,
and frequency table.
Histogram and boxplot are not appropriate for
a nominal variable.
3.3 4/25 = 16% of the respondents like “The Peto-phile” (relative frequency).
Question 3:
Name Preference Dichotomized
3.4 New variable, with the values “weird” and
“normal,” is binary/dichotomous.
3.5 Mean is 9/25 = .36 (This is the proportion of
respondents who liked weird name choices
because “weird” was the value coded 1.)
3.6 Variance = .36 x .64 = .23
V = (p)(1 – p) where p is the proportion of
cases coded 1 for the binary variable.
Questions 4, 5, and 6
4.1 Mean, median, and mode are measures of
central tendency.
4.2 They have not learned anything about
variability, dispersion, or spread. (Variance
or SD got credit but are not as good.)
5
Look at The Joy of Stats.
6
Mean gives a misleadingly high impression of
this distribution.