Statistics Flashcards
How do you calculate altered averages?
Set up before and after equations
Whats the formula for average
Sum of terms/ number of terms = average
What is the formula for weighted average?
[ Weight (value) + weight (value) ] / sum of the weights = weighted average
What is the weighted average short cut?
Subtract the largest amount in common to every quantity in your equation
Solve what remains
Add that solution to the amount that was subtracted
What is the law of weighted averages?
A weighted average of two values is always drawn closer to the heavier or more frequently occurring term
What is the median?
The middle term in a set of numbers ordered from least to greatest
How do you find the median of an even number of terms?
Put the terms in order and find the average of the two middle terms
How do you solve a fluctuating median problem?
Set up a t-chart and plug potential options for that unknown element into the set
How should you approach problems that involve the mean and median of a set of numbers?
Plug the info that youve been given into the average formula
Then simplify
What are evenly spaced number sets ?
Any set of numbers in which the gaps between the terms are the same
What is true of the mean (average) of evenly spaced number sets?
The mean always equals the median
The average of the first and last terms equals the mean and median of the entire set
What is always true of consecutive number sets ?
The mean of a set with an odd number of terms will always be an integer
What is standard deviation?
How far each number in the number set is away from the average
Whats a small standard deviation indicate?
The numbers in a set are closely bunched around the mean
If all numbers in a set are the same what is the standard deviation?
0
Whats an easy way to approximate standard deviation?
Think of it as the average difference from the mean
Find the mean of the set
Find the absolute difference between each number and the mean
Average up those differences
How do you precisely calculate standard deviation?
Calculate the number set mean Find the absolute differences of the numbers and the mean Square those differences Average the squares Find the square root of the average
What is a number that falls within a standard deviation ? give an example.
Numbers less than or equal to a certain standard deviation from the mean
I.e.
If standard deviation is 4.0 and the mean is 20
Numbers +- (16 to 24) of 20 are within that standard deviation
What is variance?
The square of the standard deviation
If you have a variance what should you do to that number to find the standard deviation ?
Take its square root
What must happen to a set for the standard deviation to decrease?
The numbers are brought closer to the mean
What must happen to a set for the standard deviation to increase?
The numbers are brought further from the mean
What happens to a sets standard deviation when you multiply each number in a set by the same amount?
The standard deviation will increase
What happens to a sets standard deviation when you divide each number in a set by the same amount?
The standard deviation will decrease
What happens to standard decimal if a number is either added or subtracted to each number in the set?
Standard deviation remains unchanged
When does standard deviation equal to 0?
When all numbers in the set are the same
When all numbers in the set are equal to the mean
What happens when you add a value that is equal to the mean to a number set?
The standard deviation is lowers
What is the key to solving maximization problems?
Consider the opposite possibility
How do you find the range of a number set?
Calculate the difference between the largest and smallest value
What happens of each term in a set is increased but the number of terms remains the same?
The mean must increase
What happens when each term in a set is increased by the same amount ?
The median must increase
What happens to the standard deviation when you add numbers that equal the mean to the number set ?
The standard deviation decreases
Weighted averages fall between…?
The largest and smallest values being averaged
