1. First Quiz Answers Undergraduate Stats Course

2. 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

3. 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.

4. 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

5. 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). 1.2Relative 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!

6. 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.

7. 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 60 th and 61 st cases both have a price tag of $50 (they happen to be cats).

8. 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.

9. 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

10. 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).

11. 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.

12. 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.