Measurement/Frequency Distribution
What level of measurement(s) can we apply for the following variable:
What do you consider your political leanings?
1 - extremely liberal
2 - liberal
3 - moderate
4 - conservative
5 - extremely conservative
This is variable is ordinal, categorical, and discrete.
Ordinal - Response categories have rank order with no clear numerical difference between categories
categorical - Data has been arranged in response categories that have been determined by researcher
discrete - no intermediate values can fall between adjacent categories. They are separate, indivisible categories
The mode is the best measure of central tendency for which level of measurement?
a. Nominal
b. Ordinal
c. Interval
A. Nominal
We have better measurements for ordinal and/or interval variables.
The range measures:
a. The average distance from the mean.
b. The average squared distance from the mean.
c. The spread of the middle 50%.
d. The spread from highest to lowest score.
d. The spread from highest to lowest score.
The normal distribution is:
a. symmetrical
b. unimodal
c. theoretical
d. all of the above
e. a and b
d. all of the above
The distribution of sample means is comprised of:
a. Infinite sample means of equal sample size
b. many variables
c. many observations of the same person
d. infinite sample means of infinite sample sizes
a. Infinite sample means of equal sample sizes
Knowing the level of measurement is important because it helps us to know which statistics to calculate:
True or False?
True - without this knowing what level of measurement something is, one cannot know what statistics can be performed. SPSS will run it, but it doesn't mean it is right.
The middle point of a distribution, where 50% falls above and 50% falls below, is called the:
a. mode
b. median
c. mean
b. Median
Why did Professor Schupp argue to you that it is better to use variance/std. deviation over the range when interpreting the dispersion of a distribution?
Both variance and standard deviation consider all cases when calculated; whereas the range only takes highest and lowest case into consideration when calculated.
A z score measures:
a. Distance from the mean in metric units
b. Distance from the standard deviation
c. Distance from the mean in units of standard deviations
d. Distance from the median
c. Distance from the mean in units of standard deviations
A distribution of sample means is:
a. an empirical frequency distribution
b. a theoretical frequency distribution
c. a sampling mean
d. none of the above
b. a theoretical frequency distribution
If 200 people out of a 500 person class got an A in Bio Class 1 -and- 50 people got an A out of a 100 people in Bio Class 2: Assuming you want to earn an A which class would you rather be randomly assigned to?
I think you’d rather be in class B because 50% got an A; whereas only 40% got an A in class A.
Remember: One must calculate relative frequencies and not just raw counts to be able to compare two distributions with different N (total size)
If the mean > median > mode, the distribution is most likely:
a. leptokurtic
b. positively skewed
c. negatively skewed
d. mesokurtic
b. positively skewed
You can only directly compare the standard deviation if:
a. the means are equal
b. the s.d. are equal
c. Neither the mean nor the standard deviations are equal
d. All of the above
e. None of the above
a. the means are equal
What proportion of cases fall within ±1 standard deviation of the mean in a normal distribution?
a. 34%
b. 68%
c. 95%
d. 99%
b. 68%
The variability of the scores in a sample tends to overestimate the variability of the scores in the population from which the sample was obtained.
True or False?
False - the variability of sample scores tends to underestimate the true variability of a population.
This is why we subtract n-1 when calculating sample level variance and standard deviation.
Cumulative percentages are not appropriate for which of the following (can be more than one):
A. Nominal variables
B. Ordinal variables
C. Internal variables
A. Nominal Variables
When a distribution of an interval level variable is skewed or has extreme outliers, which is the best measure of central tendency?
a. Mode
b. Median
c. Mean
d. None of the above
b. median - the mean is TOO sensitive to outliers; whereas the mode doesn’t take them into consideration.
The greater the variability around the mean of a distribution, the larger the:
a. Standard deviation
b. Mean
c. All of the above.
d. None of the above
a. Standard Deviation
The average number of ice cream cones eaten at Chasein Fall 2021 is 1.14 with a standard deviation of .25. What is the likelihood that you randomly select someone that ate 1 or more ice cream cones?
z-score is -.56
Probability is 71.23% (column B plus .5)
What is the shape of the following distribution of scores?
3, 10, 11, 12, 13, 15, 16, 17
Negatively skewed -
the mean is to the left of the median.
When a random sample is selected from a population, we know that, on average, the difference between the single sample mean and the population mean is predicted by…..?
Standard Error