Statistics Flashcards
Average
number of terms
In average problems when you have a value missing
use x variable and solve as how you would
When you have a variable in a term
treat it like how you would with a normal variable
sum
average * # of terms
If x and y are positive integers and x+y= 10, how can be sure of assigning the maximum possible value to y
x has the lowest possible value
- the smallest value that x can be is 1
In an evenly spaced set, the numbers in the set increase or decrease by
the same amount and therefore, share a common difference
Inclusive
include both of the numbers in the endpoints
Consecutive integers in a set that includes the first and last numbers
Highest numbers-lowest number +1
Count the number of a given number in a given range
given number )
+ 1
To find the number of terms in a set consecutive integers that includes only one of the endpoints but not both
subtract the first number from the last number
Last number - First Number
i.e: Tom is10th in line and Sara is 50th in line. How many people are there from Tom to Sar, including Tom but not Sara = 40 people
Counting the number of consecutive integers between the first and last numbers in a set
when we are interested in the number of terms between two points in a set of consecutive integers, we can subtract the first number in the set from the last number in the set and then subtract 1 from this difference
i.e: Tom is 10th in line and Sara is 50th in line. How many people are there from Tom to Sara = 40-1= 39 people
When we have an evenly spaced set of numbers
we can add the first and the last number and divide it by 2
- and this will give us the average
In an evenly spaced set with odd number of terms
the average of the terms in the set is the exact middle term of the set when the terms are in numerical order
In an evenly spaced set with even number of terms
the average of the terms in the set is the average of the middle term of the set when the terms are in numerical order
Bookend and balance point method will only work for sets of numbers in which
there is even spacing between the numbers
Weighted Average
total frequency of data points
Data point average
The weighted average of two different data points with the greater number of observations or with the greater weighted percetange
Weighted averages with percentages
Average = (percent 1) * (data point 1)+ (percent 2)* (data point 2)+..+ (percent n)* (data point n)
-> we don’t need to divide by anything because the demonimator is 100% which translates to 1
When percentage do not add upto 100%
divide by sum of the percentage that we do have
Average Speed
(Total Distance)/ Total Time
time 1 + time 2
If we know the ratio of the quantity of the two data point
we can calculate the weighted average of those data points
If the ratio of A to B were 2 to 3 -> we would express this as a/b= 2/3 and a= 2/3b
Ratio of one in comparison to the other is sufficient when determining
average
Given the value of two data points and the quantities of two data points expressed as fractions of the total number of items in the weighted average,
we can calculate the weighted average of the two data points
i. e: If the average grade of x students in a particular class is 90, what is the average grade received by the left handed students?
- > There are x/5 right handed students in the class; together, they receive an average score of 95.
Sets with an odd number of terms -> way to find the position of the median
(n+1)/2
Sets with an even number of terms -> way to find the position of the median
between:
n/2 and (n+2)/2
When we have evenly spaced set of numbers
the mean and median are equal
What are the mean and median of the first 12 positive multiple of 4
(High+Low)/2= (48+4)/2= 26
** So the mean and median is 26
Is it possible to find median even if you have unknown numbers
yes (not 100% of the time though)
Mode
Number that appears most in a data set
- > If you see one number occurring more than other one then that can be a mode
- > there can be more than one mode or sometimes no mode
Range
Highest Number in a Set- Lowest Number in a Set
Standard deviation
measures “how far” a set of values from the average of that set
- > High standard dev= most points in a data set are far from the mean
- > Low standard deviation= most of the data sets are close to the mean
- > Of all the values in the data set are same = standard dev is 0
Example of standard deviation
If the stock’s return were one standard deviation of 10 percent. If the stock’s return were -> one standard deviation then it would be [(50-10), (50+10)] = (40,60)
-> two standard deviation then it would be [(50- 210), (50+210)] = (30,70)
Standard deviation formula for range
High value = mean+ x(sd)
Low value = mean-x(sd)
Does adding or subtracting the same value to all terms does not change the standard deviation
No
i.e
A= {12, 15, 20, 21, 10}
B= {12+x, 15+x, 20+x, 21+x, 10+x}
-> If Set a has a standard deviation of n, then B also has standard deviation of n
Does Multiplying or dividing the data set by the same factor does change the standard deviation
not really, it be multiplied or divided by the same amount
-> b/c you are changing it by a constant factor
Compare the standard deviation of data set that have an equal number of data points
1) Determine the mean of each set
2) For each individual set, determine the absolute difference between the mean of that set and each data point in that set
3) Sum the absolute difference obtained from each individual set
- > The set that has the largest sum has greatest standard deviation
- > The set that has the smallest sum has s smallest tandard deviation
