Level of Measurement
3 Nominal Variables.
Examples: town name, place of birth, race, religion, ethnicity
Tip: nominal variables cannot be rank order, there is no actual number intrinsically attached to the variable, it is in name only. Nominal = name
Differences between a bar chart and histogram.
Answer: In a bar chart, the bars that represent the categories of a variable are spaced so that one bar is not directly next to another. While in a histogram, the bars actually touch one another.
Mode for the following distribution of scores is ____.
45, 9, 21, 34, 62, 97, 34
Answer: 34
Consider the variable, type of birth control practiced (for example, an IUD, condoms, none, etc).
The measure of variability is best suited to describe variation for this variable is the ____.
IQV
Suppose that the area above some Z score is 0.31, which when multiplied by 100 equals 31%.
The term for this quantity is the ____
Answer: percentile rank
3 Ordinal Variables.
Examples: satisfaction rating, letter grade (A, B, C etc.), class rank (freshman, sophomore, etc.)
Tip: ordinal = ordered
Difference between frequency distributions for nominal and ordinal variables.
The order in which the categories are listed. Ordinal variables must be ascending or descending. Nominal variables do not need to be in any specific order.
The median for this distribution is ____.
14, 4, 12, 7, 10, 9
Answer: 9.5
The range for the following scores is ____.
26, 25, 18, 92, 87, 43, 44
Answer: 74
The percentage of the area under the normal curve falls between ±1 standard deviations is ____.
Answer: 68.26
3 Interval Ratio Variables.
Examples: age, actual income, percentage scored on a test
Tip: Interval-ratio = actual numbers
About 13% of survey respondents in a sample reported that they do not attend religious services regularly.
The proportion of survey respondents who report attending religious services regularly is _____.
Answer: 0.87
To get this:
100% - 13% = 87% / 100 = .87
The mean for this distribution is _____.
14, 4, 12, 7, 10, 9
Answer: 9.33
What information does a box plot visually present?
range, IQR, median, minimum/lowest score, maximum/highest score
Show the class how to calculate Z scores on the whiteboard.
On the whiteboard.
Explain dichotomous variables and provide two examples.
Yes/No
Married/Unmarried
Employed/Unemployed
A survey of 3,055 respondents asked whether or not anyone had been widowed. Eighty persons responded “yes.”
The percentage of respondents that have never been widowed is ______.
Answer: 97.38%
To get this:
3055 - 80 = 2975
2975/3055 = .9738 x 100 = 97.38%
The measure of central tendency that is more susceptible to extreme values is the _____.
Answer: mean
Explain what the IQR is and how to find it.
The middle 50% of the distribution.
Q3 - Q1 = OQR
75% - 25%
In a sample, the mean is 70.07 and the standard deviation is 10.27.
Find the Z score that corresponds to a raw score of 80.
Answer: 0.97
To get this answer use the formula to find Z.
Compare and contrast discrete variables and continuous variables. Provide two examples for each.
Discrete Variable Examples: number of children, number of people in a class. Tip: Discrete variables cannot be subdivided.
Continuous Variable Examples: length, age, temperature, weight, speed, time. Tip: these can be broken down into smaller and smaller units
In a sample of 310 people, 186 completed only high school, 24 completed only some college, 93 completed a two-year or four-year college, and 7 attended graduate school.
You need to find the proportion of the sample that has some college or more.
Answer: 0.4
To get this:
Add some college = 24 + 93 + 7 = 124
124/310 = 0.4
For the following data, compare the mode, median, and mean.
11, 43, 84, 55, 2, 13, 9, 32, 2, 14, 21, 11, 2
Answers:
mode = 2
median = 13
mean = 23
The standard deviation for the following distribution:
100, 99, 56, 62, 88
20.74
Scores for an exam are normally distributed with a mean of 235 and a standard deviation of 52.
Find the area beyond for a score of 287.
Z = (287-235) / 52 = 52/52
Z = 1
In Appendix B find a Z score of 1.
Find the area beyond Z.
0.1587.