Math Review - Data Analysis Flashcards
How do you calculate the interquartile range?
EX: 2, 4, 4, 5, 7, 7, 7, 7, 7, 7, 8, 8, 9, 9, 9, 9
It is the difference between the third quartile and the first quartile, Q3 - Q1
Q1 = 6
Q3 = 8.5
8.5 - 6 = 2.5
How do you calculate the range?
EX: 6,4, 7, 10, and 4
The range of the numbers in a group of data is the difference between the greatest number G in the data and the least number L in the data, that is, G - L.
10 - 4 = 6
How do you calculate the standard deviation for the five data 0, 7, 8, 10, and 10
1st) Find the mean which is 7
2nd) Then, determine the sqaure differences from the mean:
(7-0)2, (7-7)2, (7-8)2, (7-10)2, (7-10)2
or 49, 0, 1, 9, 9.
3rd) Next, find the average of the sqaured differences 68/5 or 13.6
4th) Take the nonnegative sqaure root of the average sqaured difference. The positive square root of 13.6 is 3.7
* Note: for SAMPLE standard deviations you divide the sum of the sqaured difference by n-1 instead of n*
Frequency or count
The number of times that the category or value appears in the data
0!
1
How do you calculate the mean?
EX: 6,4, 7, 10, and 4
Take the sum of the n numbers and divide it by n
6+4+7+10+4 / 5 =
31/5 =
6.2
How do you calculate the mode?
EX: 6,4, 7, 10, and 4
The mode is the number that occurs most frequently in the list.
4
A list of numbers may have more than one mode. For example, the list 1, 2, 3, 3, 3, 5, 7, 10, 10, 10, 20 has two modes, 3 and 10
How do you calculate the median?
EX: 6,4, 7, 10, and 4
First order the numbers from least to greatest.
The median is the middle number in the order. If n is even, then there are two middle numbers, and the median is the average of these two numbers
6
Mutually Exclusive
Events that cannot occur at the same time
Expected value
Another name for the mean of a random variable
What does 4! =
4! = (4)(3)(2)(1) = 24
How many different five-digit positive integers can be formed using the digits 1, 2,3, 4, 5, 6, and 7 if none of the digits can occur more than once in the integer?
7!
______ =
(7-5)!
(7)(6)(5)(4)(3)(2!)
________________ =
2!
(7)(6)(5)(4)(3) =
2520
Independent
The occurrence of either event does not affect the occurrence of the other
The number of times that the category or value appears in the data
Frequency or count
