Ch. 13 Statistics Flashcards
Average =
Sum of terms / # of terms
SUM =
Avg x # of terms
Number of consecutive integers formula, inclusive
= Highest Number - Lowest + 1
Number of consecutive integers formula, exclusive
= Highest Number - Lowest - 1
Number of consecutive integers formula, including one endpoint only
= Highest Number - Lowest
of multiples of given number formula
= [(Highest multiple - Lowest multiple) / Given number] + 1
+1 b/c you’re including both endpoints (highest & lowest multiple)
The methods for getting average efficiently
Evenly spaced sets ONLY
Midpoint - figure out median position
Bookend - average = (first + last) / 2
How would you solve this: what is the sum of odd integers from 5 to 55, inclusive?
- Avg = SUM / #, so we know SUM = avg x #
- Get average of odd integers from 5 to 55. Because it’s evenly spaced, we can do bookend method: (55 + 5) / 2 = 30
- Get # of terms - we need all ODD integers: (55 - 5)/2 + 1 = 26
- Plug into formula: SUM = Avg x # = (30)(26) = 780
Formula for “how many multiples of 2 or 3 from 1 to 90, inclusive?”
= Multiples of 2 + Multiple of 3 - Multiples of LCM (2,3)
(B/c we want to remove the double counted multiples)
What if the question asks for multiples of 2 or 3 but NOT BOTH? What is the formula?
= Multiples of 2 + Multiples of 3 - (2 x Multiples of LCM(2,3))
Weighted Avg formula
Same as average = SUM / # of items
When you’re doing weighted avg, think of PER (e.g., “the score PER student”)
Median formula
It’s the number in the (n+1)/2 position
When is mean = median?
IN evenly spaced sets
What is mode?
Number that occurs most frequently
What is the mode if each number occurs the same number of times? e.g., S = {1, 1, 2, 2, 4, 4}
There is no mode
Can there be more than one mode?
Yes! If two or more numbers occur MORE frequently than others, then all of these numbers are modes
Range = ?
Highest - Lowest number in the set
What does standard deviation measure?
How far values in the set are from the average/ mean of the set
If the mean is 85 and one standard dev is 5, what amount falls within one standard deviation?
85 +/- 5
= 80 to 90
What happens to standard deviation if you +/- the same amount to each element in data set?
Std dev remains the same
{500, 700, 650, 900} has same std dev as
{501, 701, 651, 901}
What happens to standard deviation if you multiply/divide by the same amount to each element in data set?
The std dev will also be multiplied/ divided by that amount
What is the lowest possible standard deviation?
zero
When does a set have a standard deviation of 0?
When all the elements in the set have the same value
How do you decrease a positive standard deviation?
Add elements to the set that are = to the mean
