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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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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

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.

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!

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.

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).

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.

It relates to a new data file of survey results:

Cases are respondents

Variable is NAME PREFERENCE

Values are the specific names

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

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.