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
What is the standard deviation of this set: {15, 15, 15}?
0
When range = 0, what is the std dev?
Also 0, because when range = 0, highest = lowest = mean, all the elements in the set are the same value
When the highest value = mean, what is the std deviation?
This means all values in the set are the same (otherwise highest or lowest cannot equal mean), so std dev = 0
If the range is not 0, can the std dev be 0?
No. If range is not 0, if largest does not equal smallest, then the elements of the set are NOT the same, and std dev cannot be 0. Std dev is GREATER than 0.
