Ch. 8 - Statistics and Sets Flashcards
Mean
The average value of a set — also called the arithmetic mean.
Median
The middle value of a set.
First put all the elements in order, then find middle. If even number of elemets, find the average between the two middle values.
Mode
The value that occurs most often in a set.
Range
The positive difference between the set’s highest and lowest values.
Stem-and-leaf plot for the data:
65, 70, 70, 78, 80, 81, 84, 86, 89, 89, 93, 93, 93, 98, 100.
Box plot for the data:
65, 70, 70, 78, 80, 81, 84, 86, 89, 89, 93, 93, 93, 98, 100.
A boxplot shows the data broken into quartiles. Each part of the boxplot represents 25% of the data. The interquartile range is the range of the middle 50%: Q3 – Q1, or the width of the box.
In this example, that’s 93 – 78 = 35
Standard Deviation
A measure of how far the typical value in a set is from the set’s average. The bigger the SD, the more widely dispersed the values are. The smaller the SD, the more closely grouped the values in a set are around the mean.
How far from the SD?
To find how any deviations above or below the mean a number is, find the differenece between the mean and the number you’re dealing with; then divide it by the SD.
Probability of x =
number of outcomes that are x ÷ total number of possible outcomes
You can find the probability that something WILL NOT happen by subtracting the probability that it WILL happen from 1.
The probability of multiple events occuring together is the product of the probabilites of the events occuring individually.
I.e.
The probability of thowing two heads in a row is
1/2 * 1/2 = 1/4.
Permutation
nPr = ?
(n = total number, r = selected number)
An arrangement of distinct objects in a definite order.
nPr = n! / (n – r)!
Combination
nCr = ?
(n = total number, r = selected number)
A grouing of distinct objects in which order is not important.
nCr = n! / r!(n – r)!
5! / (6! – 5!) = ?
1 / 5
Group Problem Formula
Total = Group 1 + Group 2 + Neither – Both
