Statistics module 5 Flashcards
How does the formula for finding the standard deviation of random variables differ from finding the standard deviation
When finding the standard deviation for random variables use the formula: standard deviation of random variable = square root of ((random variable value quantity - mean) squsred multiplied by probability of getting that random variable value (how many outcomes have this quantity of the random variable)) find this value for each random variable quantity and add them all together
whereas formula for finding the standard deviation = square root of (((the quantity of the option - mean quantity of options)squared) divided by the total number of options)
Standard deviation just looks at the average distance between each option but not the frequency of each option whereas standard deviation of random variables looks at the distance between each option and the likelihood of getting each distance, since you can find the probability of getting more then 2 or options by adding the probabilities of each options if they are disjoint, and for random variables they are disjoint, (as can not have 2 diff quantities of proprtion - ones with same porportion are accounted for in probability) so finds the or probability of getting each porportions distance from the mean
What does sample mean
A representation of the total population we are interested in whose presence of a characteristic we examine in hopes that we can generalize it to the whole pop
What does population mean
The total amount of people we are looking for the presence of the characteristic in
What does population porportion and sample porportion mean
population porportion means the ammount of people with the characteristic of interest in the population
What does the sample porportion mean - the ammount of people with the characteristic of interest in the sample
How can we use distribution tables for sample porption
Can have one (x) colomn represent the proportion, (quantity of characteristic of interest in sample) and the other colomn represent the likelihood of getting this porportion, (how many outcomes out of the total possible outcomes have this porportion) can also do this for the mean can take the mean porportion of a group of samples and then find the propbability of getting a group of samples with this mean porportion, (how many groups of samples out of the total number of groups of samples have this mean porportion)
How do you find the mean and standard deviation of a characteristic of interest out of all samples
Since we are looking at the likelihood of getting a specific characteristic not just the average of all options use the expected variable formula
Expected variable formula for mean = quantity of characteristic in x1 multiplied by the probability of getting x1, (how many out of total outcomes have this quanity) find this value for all outcomes and add them together - finds or probability of getting each porportion
formula for standard deviation random variable = square root of ((x, (where x is quantity of specific characterstic) - mean)squared) multiplied by probability of x quantity, (how many out of total outcomes feature this x value) find this value for all x values and add them all together, this way you are finding the or probability of getting each distance from the mean.
When can the mean of a sample porportion = the porportion of the population
In order for the mean of the sample porportion to = the population porportion it must
1. Have the porportions found in each individual in the sample be independent from each other
2. Have the sample porportion be less then 10% of the population, (very unlikley to be able to get a sample porpotion larger then this) bc if so is large enough where answeres start to become dependent on each other, (who was selected)
3.Have the number of observations multiplied by the mean of sample porportion is equal to or greater then 10 and when the mean of the sample porportion multiplied by (sample porportion -1) is equal to or greater then 1
When will a sample porportion have a normal distribution, (unimodal, symmetric, mean= median = mode) and when will it not and how do you find out the shape and center of sample porportions graph if it does not have normal distribution
A sample porportion will have a normal distribution if the mean of the sample porprotion multiplied by the number of observations is equal to or greater then 10 and the mean of the sample porportion multiplied by the mean of the sample porportion - 1 is equal to or greater then 10, if these conditions are not met then you will have to use distribution tables to find center and shape or the sample porportions, you can also use z scores, (x - mean) divided by stan dev, to find out probability of getting certain outcomes.
