14 - Statistics Flashcards
Counting consecutive integers, inclusive of the first and last numbers in a set
(Highest number - lowest number + 1)
50 to 101, inclusive
101 - 50 + 1 = 52
Counting the number of consecutive inegers inclusive of either only the first or last number in a set, not both.
Tom is 10th in Line , and Sara is 50th in line. How many people are there from Tom to Sara, including Tom but not Sara?
Counting the number of consecutive inegers inclusive of either only the first or last number in a set, not both.
Last/highest number - given first number
Tom is 10th in Line , and Sara is 50th in line. How many people are there from Tom to Sara, including Tom but not Sara?
50 - 10 = 40
Counting the number of integers in a set between 2 numbers
Counting the number of integers in a set between 2 numbers
Last/highest - first number - 1
Counting multiples of integer A AND B, but not of both, in a set of consecutive integers where remainder is needed
What is the sum of all two-digit numbers that leave a remainder of 1 when divided by both 3 and 4?
Counting multiples of integer A AND B, but not of both, in a set of consecutive integers
What is the sum of all two-digit numbers that leave a remainder of 1 when divided by both 3 and 4?
Find the LCM and add one because you need a remainder of 1
LCM (3,4) = 12 + 1 = 13
sum = average * quantity
average = (first integer + last integer / 2)
first integer = LCM (3,4) + remainder = 12 + 1 = 13
last integer = LCM * n + remainder needed where n will give you the product closest to the highest boundary (in this case 99) 12*8=96 + 1 = 97
13 + 97 / 2 = 55
Quantity = ((last integer - first integer) / common difference) + 1
(97 - 13) / 12 = 7 + 1 = 8
55*8 = 440
Counting multiples of integer A or B, but not of both, in a set of consecutive integers
Counting multiples of integer A or B, but not of both, in a set of consecutive integers
Number of multiples of A - Number of Multiples of B - 2(Number of Multiples of LCM)
Counting the multiples of integer A or B in a set of consecutive integers
Counting the multiples of integer A or B in a set of consecutive integers
(Number of multiples of A + Number of Multiples of B) - (Number of Multiples of the LCM A,B)
Counting consecutive multiples in a set
Counting consecutive multiples in a set
((Highest number divisible by given number - lowest number divisible by given number) /given number)) + 1
If the smallest or largest value in a data set is the mean, then
If the smallest or largest value in a data set is the mean, then
all values in the data set are the same
If range = 0 for a data set, then
If range = 0 for a data set, then
all values in the data set are the same
Using the average formula to find the sum of a set of numbers
Using the average formula to find the sum of a set of numbers
Sum = (Average * Number of Terms)
Finding the arithmetic mean with evenly spaced integers
Weighted Average Formula
Weighted Average Formula
(data point 1 * frequency of data point 1) + (data point 2 * frequency of data point 2) /total frequency of data points
Boundaries of Weighted Average
Boundaries of Weighted Average
The weighted average of two different data points will be closer to the data point with the greater number of observations with the greater weighted percentage.
Weighted Average Data Sufficiency Warning
Weighted Average Data Sufficiency Warning
You don’t need a total number when comparing weighted percentages
Weighted Time Average
Weighted Time Average
Total Distance/Total Time
Using Ratios and Fractions when solving Algebra
Median
Odd
Middle Number in a Set
Odd number of terms in a set - middle number
Even number of terms in a set - average of two middle numbers
Shortcut to finding median’s position in a large set
Shortcut to finding median in a large set
Odd number of terms in a set: (n+1/2) = position in set
Even number of terms in a set: (n+2/2) = position of the 2nd number in the set
Relationship between mean and median in an even set of numbers
Relationship between mean and median in an even set of numbers
mean = median in an even set of numbers
Mode
Mode
Number that occurs most frequently
Can be multiple if more than one number has the highest frequency
No mode if no number appears more than the other numbers
Range formula
Range formula
(highest number in a set - lowest number in a set)
Standard Deviation
- Standard Deviation measures how far a set of values are from the mean
- higher SD when further from mean
- lower SD when closer to the mean
- if numbers = mean, SD = 0
- typically look at SD = 1 or 2 or 3, beyond that is very unlikely to occur
Adding or subtracting one constant value to each term in a data set does what to the standard deviation?
Adding or subtracting one constant value to each term in a data set does what to the standard deviation?
Nothing, but it does change the mean
Caveat: if SD = mean, it will decrease
If you multiply or divide the elements in a data set by a constant amount, the standard deviation will
If you multiply or divide the elements in a data set by a constant amount, the standard deviation will also be multiplied or divided by that same amount
Adding numbers to a data set equal to the mean will to what to a positive standard deviation?
Adding numbers to a data set equal to the mean will to what to a positive standard deviation?
Decrease the standard deviation
Comparing standard deviations through estimation
Comparing standard deviations through estimation
Given sets of numbers
- Find the mean in a set
- Determine absolute value of each number from the mean
- Add together
- Do this for each set, higher number = higher SD
If given a data set of equal values, the standard deviation is
If given a data set of equal values, the standard deviation is zero.
The standard deviation will be zero when
- Range of a set = 0
- Largest value of a set = mean
- Smallest value of a set = mean
Relationship between mean and median in an even set of numbers
mean = median in an even set of numbers
Solving for standard deviation and mean given two standard deviations and values:
Ata track meet, a measurement in the standing long jump of 12.5 feet was 3.5 standard deviations above the mean; a measurement of 2.5 feet was 1.5 standard deviations below the mean. What was the mean measuremnet of the standing long jump?
Solving for standard deviation and mean given two standard deviations and values:
Ata track meet, a measurement in the standing long jump of 12.5 feet was 3.5 standard deviations above the mean; a measurement of 2.5 feet was 1.5 standard deviations below the mean. What was the mean measuremnet of the standing long jump?
m = mean, s= standard deviation.
Equation 1: m + 3.5s = 12.5
^It is addition because it is above the standard deviation.
Equation 2: m - 1.5s = 2.5
^It is subtraction because it is below the standard deviation.
Data Sufficiency: Averages with variables
Sum of Arithmetic Progression of Consecutive Integers (a sequence of numbers that all differ by a given number)
Sum of Arithmetic Progression of Consecutive Integers (a sequence of numbers that all differ by a given number)
sum = average * quantity
average = (first integer + last integer)/2
quantity = (last integer - first integer/common difference) +1
Don’t forget the +1!
What number should be removed from the list 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 so that the average of the remaining number is 6.9?
What number should be removed from the list 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 so that the average of the remaining number is 6.9?
12 - 2 + 1 = 11 numbers in the list
Average =7
Average is the median since it’s an odd set of numbers.
7*11 = 77
(77 - 8) / 10 = 6.9 so 8 needs to be removed
Arithmetic mean of a consecutive set (bookend approach)
Arithmetic mean of a consecutive set (bookend approach)
(smallest integer + largest integer) / 2
The cost of two items and the average price are sufficient to calculate the ratio or percentage.
