Statistics Flashcards
(37 cards)
there are many problem variations that can occur where you need to use the arithmetic mean formula where you may be given the mean, and then a variable is inserted into the (sum of set of elements)/(# of elements) part
arithmetic mean?
sum of set of elements/ # of elements
how do you deal with situations where you are total group is broken up and you are given information about averages of sub components of the group and about the group as a whole and asked for average information about the other subcomponent
what is an evenly spaced set
numbers in the set increase or decrease by the same amount, and thus, share a common difference
how do you count the number of consecutive integers in a set (inclusive of the first and last elements)?
highest number - lowest number +1
ex: how many numbers from 50 to 101 inclusive? 101-50+1=52
how do you count # of consecutive multiples in a set, inclusive?
((highest # divisible by the multiple - lowest # divisible by the multiple)/multiple number)+1
ex: number of multiples of 3 between 1 and 100 inclusive is (100-1)/3 + 1
how do you count the number of consecutive items in a set (including only one of the end points of the set)?
simply subtract smallest number in the set by the biggest number
how do you count the number of consecutive integers between the first and last numbers in a set
biggest - smallest - 1
what is the bookend method for finding the arithmetic mean?
if you have a set of evenly spaced numbers, the arithmetic mean is (largest+smallest)/2
what is the balance point method for finding the arithmetic mean?
for set with even number of terms: balance point method means you find the two middlemost terms and take their average
for set with odd number of terms: average of the set is the middlemost point
how do you calculate the number of multiples of A or B in a set of consecutive integers?
multiples of A + # multiples of B - # multiples of LCM(A,B)
LCM(A,B) must be removed since those numbers will be duplicated in each list and we want them to only appear once
how do you calculate the number of multiples of A or B BUT NOT OF BOTH in a set of consecutive integers?
[multiples of A] + [# multiples of B] - 2*[# multiples of LCM(A,B)]
similar to calculating the number of multiples of A or B, but you must remove all instances of the LCM(A,B) by removing it twice
weighted average = ?
((data pt 1)(frequency of data pt 1)+(data pt 2)(frequency of data pt 2) + ….)/(total frequency of data points)
what assertions can be made about a weighted average when there are differences in the frequency of a certain data point?
the weighted average of two different data points will be closer to the data point with the greater frequency, number of observations, or weighted percentage
how can you still calculate weighted averages if all you have is the data points and the ratio of the prevalence of the two groups?
given the value of two data points and the ratio of the quantity of the two data points, we can calculate the weighted average
what is the median of a set of numbers?
if set has an odd number of items: it is the number that is exactly in the middle after the set has been ordered
if set has an even number of items: order the set of numbers, then take the average of the two middle numbers - that is the median
how do you quickly determine the POSITION of the median of a large ordered set with an odd number of items?
for a set with n items (where n is odd), the median is in the (n+1)/2 position of the ordered set
how do you quickly determine the POSITION of the median of a large ordered set with an even number of items?
for a set with n items (where n is even), the median the average of the values at the (n+2)/2 and n/2 positions of the ordered set
when are the mean and median of a set of numbers the same?
if the set of numbers is equally spaced
what is the mode?
the number that occurs most frequently in a set
can a set have more than one mode?
yes, if two or more numbers appear more frequently in a dateset than other numbers they are all modes
can a dataset have no mode?
yes, if all numbers occur with the same frequency
What is the range of a dataset?
[highest value in set] - [lowest value in set]
what does standard deviation measure?
how far a set of values are from the arithmetic mean of that data set