Data Types and Miscellaneous
(1.2)
(1.2)
What type of data is used in Likert scales?
Ordinal
What is the ideal type of sample we desire in any statistical study, one in which all members of the population have an equal likelihood of being selected?
Simple Random Sample
Explain, in order, how to find the IQR given a list of values.
Put in order, find Q1 and Q3, then subtract Q3-Q1.
How do you calculate a z-score?
Your value (x) minus the mean (mu), then divided by the standard deviation (sigma).
True or False, to get the mean of the sample, you divide the standard deviation by the square root of the sample size. EXPLAIN!
False, dividing standard deviation by the square root of the sample size is STANDARD ERROR.
True or False: We can represent categorical data using a histogram, use a complete sentence to defend your answer.
False, we can only represent numerical data in a histogram.
Explain how stratified random sampling works.
In stratified sampling, we split the population into clusters or groups, then select a random sample from each of those clusters.
Using your WORDS, explain the processes of calculating the standard deviation.
Find the mean, subtract the mean from each value, square each, add, divide by n-1, square root.
How do you find the p value (proportion) once you have your z score?
You use the z-table to look up the p value (proportion), by using the z-score values.
How does increasing the sample size affect the standard error of the sampling distribution?
Increasing the sample size decreases the standard error, making the estimates more precise.
Data:
72, 88, 91, 84, 77, 95, 89, 83, 90, 86, 80
CALCULATE THE FIVE NUMBER SUMMARY
MINIMUM=72
Q1=81.5
MEDIAN=86
Q3=89.5
MAXIMUM=95
When studying whether serving ice cream and number of drownings are related, a statistician realizes there is, in fact, a correlation. To imply causation, they would be failing to account for what type of variable?
Confounding variable (summer months)
DAILY DOUBLE -- 600 POINTS
How do you know when to use the mean/SD or median/IQR to represent the center and spread of the data?
Approximately Normal Data = mean/SD
Skewed Data = median/IQR
The empirical rule says that roughly 68% of the data should be how close to the mean?
Within one standard deviation (above or below).
Explain Central Limit Theorem.
The Central Limit Theorem says that the distribution of sample means becomes approximately normal as the sample size gets large (n=20) OR the population is an approximately normal distribution already.
Data:
12, 18, 25, 30, 31, 36, 40, 42, 47, 50
CALCULATE THE FIVE NUMBER SUMMARY
MINIMUM=12
Q1=25
MEDIAN=33.5
Q3=42
MAXIMUM=50
We want to survey a sample of seniors to determine which prom themes are desired this year. Explain the Variable/Parameter of interest and the sampling statistic in this scenario.
Variable/Parameter of interest = prom theme choices of all seniors
Sampling statistic = prom theme choices of only those seniors surveyed.
The following 11 test scores were recorded in a class:
72, 88, 91, 84, 77, 95, 89, 83, 90, 86, 80
Calculate the mean score.
SUM = 935
935/11
MEAN SCORE IS 85
If you want the percentage of the data greater than a particular value, how do you calculate that percentage?
Using the z score, find the percentage/proportion then subtract that percentage/proportion from 100%/1.000.
A population has a standard deviation of 12. If you take a random sample of 36 people, what is the standard error of the sample mean?
Sigma = 12 n = 36
12/square root of 36
12/6
Standard error is 2.
Explain the relationship between mean and median for an APPROXIMATELY NORMAL, RIGHT SKEWED, AND LEFT SKEWED distribution.
APPROXIMATELY NORMAL: MEAN=MEDIAN=MODE
RIGHT SKEWED: MEAN > MEDIAN
LEFT SKEWED: MEAN < MEDIAN
Explain voluntary response bias.
Voluntary response bias happens when the people who choose to participate in a survey are different from the overall population, usually because they feel strongly about the topic, so the results end up skewed.
Data: 4, 7, 9, 10, 10
Find the standard deviation.
MEAN = 8
DIFFERENCES SQUARED (4-8)^2=16, (7-8)^2=1, (9-8)^2=1, (10-8)^2=4, (10-8)^2=4
SUM OF DIFFERENCES SQUARED (16+1+1+4+4)=26
SUM DIVIDED BY N (26/4)=6.5
SQUARE ROOT OF 6.5
STANDARD DEVIATION IS 2.55
USE YOUR WORDS:
How would I find the z-score for the 80th percentile?
Find the closest proportion near 0.800, then work backwards to find the z-score...then the initial value.
DAILY TRIPLE
A population has a standard deviation of 28. You want the standard error of the sample mean to be no larger than 4. What is the sample size required?
SE = 4 SIGMA = 28
4=28/SQUARE ROOT OF N
4(SQUARE ROOT OF N)=28
SQUARE ROOT OF N = 7
N = 49