Download KNR445: Class exercises week 1 (measurement levels, central

[KNR445: CLASS EXERCISES WEEK 1 (MEASUREMENT
January 21, 2009 LEVELS, CENTRAL TENDENCY, SPREAD, NORMAL CURVES)]
Class exercise set 1: Measurement Levels (or scales)
A. Name the measurement level for each of these variables (and say why
you chose your answer):
1. Average score at bowling for each player in a bowling league
ratio
2. Placement in a bowling league
ordinal
3. All the team names in the bowling league
nominal
4. Average speed at which each player in the bowling league bowls the
ball
ratio
5. Bowling skill knowledge, as measured by a survey given to all bowling
league members (survey was multiple choice, had 30 questions, and
generated a score between 0 and 30).
interval
6. The score on the above test (just as a score, not as a measure of
knowledge)
ratio
B. Let’s say you have knowledge of ranks, and want to convert it to a ratio
scale. Can you legitimately do this, without any extra information?
no
Class exercise set 2: Central tendency, spread, normal
curves
1. What are the mean, median, and mode of the following set of numbers?
3, 4, 1, 2, 4, 4
Mean = 18/6 = 3
Mode = 4
[KNR445: CLASS EXERCISES WEEK 1 (MEASUREMENT
January 21, 2009 LEVELS, CENTRAL TENDENCY, SPREAD, NORMAL CURVES)]
Median = 3.5 (3+4/2)
2. Which set of numbers has the largest mean? The highest median? The
highest standard deviation?
3, 4, 1, 2, 4, 4
or
1,1,1,7,7,7
Largest mean = 111777 = 4
Highest median = 111777 = 4 (1+7/2)
Highest SD = 111777 (look at sum of absolute deviations from
mean: for 123444, mean is 3, so sum of abs deviations is:
2+1+0+1+1+1 = 6. For the other one, sum of abs devn is: 3+3+3+3+3+3
= 18)
3. Which of the above sets is bimodal?
111777
4. If you have a distribution with a mean of 50 and a SD of 10, what’s the
probability of getting these values:
a. inside the range 40 to 60
40 to 60 = +/- 1SD, so inside is 68%, or 0.68
b. outside the range 40 to 60
40 to 60 = +/- 1SD, so inside is 68%, or 0.68. So outside is 1-0.68 = 0.32 or 32%
c. outside the range 50 to 70
30 to 70 = +/- 2SD, so inside is 95%, or 0.95.
50 to 70 = ½ of 30 to 70 = 95%/2 = 47.5%
So outside of 50 to 70 = 100% - 47.5% = 52.5%
d. less than 50
50 is the mean or central point, so less than that is 50% or 0.5
e. more than 60
60 is 1SD above the mean. So from the mean to 60 is 0.34, or 34% (68%/2). So
the area above that is 0.50 – 0.34 = 0.16, or 16%
5. You have 2 distributions. You analyze their structure, and find that the
first (a) is normally distributed, and the second (b) is positively skewed.
[KNR445: CLASS EXERCISES WEEK 1 (MEASUREMENT
January 21, 2009 LEVELS, CENTRAL TENDENCY, SPREAD, NORMAL CURVES)]
What would be the appropriate measures of central tendency and spread
to choose for each of them?
a. Mean, SD
b. Median, Semi-interquartile range
6. In a normal distribution, what measure of central tendency occurs most
frequently? What measure of central tendency has the greatest
magnitude?
All of them (same answer for both – they are all equal)
7. In a positively skewed distribution, what measure of central tendency
occurs most frequently? What measure of central tendency has the
greatest magnitude?
Mode, Mean.