First Quiz AnswersGraduate 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”

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