Statistics Flashcards
What ist the formula for the mean?
Sum of terms / number of terms
What is the Median, and how do you find it?
If the number of terms (which should be arranged from least to highest) is Even, then take the average of the two numbers in the middle
If the number of terms (which should be arranged from least to highest) is Odd, then number is the middle is the Median
What is the mean if you combine terms with the same mean?
Ex. Set D is a new set created by combining all the terms of sets A,B,C, each have a median of 125. What is the median of D?
When you combine sets with the same Median, the median of the new set will ALWAYS be the same as the median of the smaller sets.
When does the mean = the median?
When the terms are evenly spaced. When there is an order, the median is the same as the mean
How can you know the mean and median of an evenly spaced set, such as this:
Set A : 2,x,y,z,24
This is only possible when it is EVENLY SPACED.
Sum the first an last term and divide by two
(24 + 2) / 2 = 13
How can you know the sum of the terms?
Set A: 2,X,Y,XZ,24
Use Gauss-s formula
N= number of terms
N (First term + last term) / 2
5 (26) / 2 = 65
What is N if they tell you: ….. all even integers from 650 to 750?
N = (last term - first term / 2 ) + 1= 51
How do you determine the range of numbers if you only want even or odd?
Objetive: Adjust the range so that it begins and ends with the type of number you want (either even or odd)
1.- Even numbers:
- If the range starts with an odd number, move to the next even number
- Uf the range ends with an odd number, move to the previous even number
1.- Odd numbers:
- If the range starts with an Even number, move to the next odd number
- Uf the range ends with an Evem number, move to the previous odd number
What is the mode?
The mode is the most frequently occurring value in a set.
What is the range or a set of values?
The range of a set is the difference between the largest and the smallest value in a set.
Largest value - smallest value
What are 3 propoerties from ranges?
1.- Ranges cannot be negative
2.- If the range of a set is zero, then all numbers in the set must be zero
3.- Changing any value other than the SMALLEST and the LARGEST, has no effect in the range
What are the steps for finding a standar deviation of a set?
1.- Find the Mean: Add all the values and divide by the number of values.
2.-Compute Differences: Find the difference between each value and the mean.
3.- Square Differences: Square each of these differences.
4.- Average of Squared Differences: Sum up the squared differences and divide by the number of values.
5.-Square Root: Finally, take the square root of the average squared difference to get the standard deviation.
What happens to a Standard Deviation when you multiplicate?
- Multiplying each term of a set by a number with an absolute value greater than 1 increases the standard deviation, while multiplying by a number with an absolute value less than 1 decreases the standard deviaton
What happens to a Standard Deviation when you divide?
- Dividing each element in a set by a number with an abolute value greater than 1 decreases the Standard Deviation, while diving by a number with an absolute value less than 1 increases the standard deviation.
What happen to a Standard Deviation when you change the sign of all elements?
- Changing the sign of all elements in the set or multiplying by -1, has no effect on the Standard Deviation
