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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?

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thinking about question 1 1
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
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
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
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
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
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
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
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
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 Pet-o-phile” (relative frequency).

question 3 name preference dichotomized
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
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.