Statistics

Question 1

Average

Answer 1

number of terms

Question 2

In average problems when you have a value missing

Answer 2

use x variable and solve as how you would

Question 3

When you have a variable in a term

Answer 3

treat it like how you would with a normal variable

Question 4

sum

Answer 4

average * # of terms

Question 5

If x and y are positive integers and x+y= 10, how can be sure of assigning the maximum possible value to y

Answer 5

x has the lowest possible value

- the smallest value that x can be is 1

Question 6

In an evenly spaced set, the numbers in the set increase or decrease by

Answer 6

the same amount and therefore, share a common difference

Question 7

Inclusive

Answer 7

include both of the numbers in the endpoints

Question 8

Consecutive integers in a set that includes the first and last numbers

Answer 8

Highest numbers-lowest number +1

Question 9

Count the number of a given number in a given range

Answer 9

given number )
+ 1

Question 10

To find the number of terms in a set consecutive integers that includes only one of the endpoints but not both

Answer 10

subtract the first number from the last number
Last number - First Number

i.e: Tom is10th in line and Sara is 50th in line. How many people are there from Tom to Sar, including Tom but not Sara = 40 people

Question 11

Counting the number of consecutive integers between the first and last numbers in a set

Answer 11

when we are interested in the number of terms between two points in a set of consecutive integers, we can subtract the first number in the set from the last number in the set and then subtract 1 from this difference

i.e: Tom is 10th in line and Sara is 50th in line. How many people are there from Tom to Sara = 40-1= 39 people

Question 12

When we have an evenly spaced set of numbers

Answer 12

we can add the first and the last number and divide it by 2

- and this will give us the average

Question 13

In an evenly spaced set with odd number of terms

Answer 13

the average of the terms in the set is the exact middle term of the set when the terms are in numerical order

Question 14

In an evenly spaced set with even number of terms

Answer 14

the average of the terms in the set is the average of the middle term of the set when the terms are in numerical order

Question 15

Bookend and balance point method will only work for sets of numbers in which

Answer 15

there is even spacing between the numbers

Question 16

Weighted Average

Answer 16

total frequency of data points

Question 17

Data point average

Answer 17

The weighted average of two different data points with the greater number of observations or with the greater weighted percetange

Question 18

Weighted averages with percentages

Answer 18

Average = (percent 1) * (data point 1)+ (percent 2)* (data point 2)+..+ (percent n)* (data point n)

-> we don’t need to divide by anything because the demonimator is 100% which translates to 1

Question 19

When percentage do not add upto 100%

Answer 19

divide by sum of the percentage that we do have

Question 20

Average Speed

Answer 20

(Total Distance)/ Total Time

time 1 + time 2

Question 21

If we know the ratio of the quantity of the two data point

Answer 21

we can calculate the weighted average of those data points

If the ratio of A to B were 2 to 3 -> we would express this as a/b= 2/3 and a= 2/3b

Question 22

Ratio of one in comparison to the other is sufficient when determining

Answer 22

average

Question 23

Given the value of two data points and the quantities of two data points expressed as fractions of the total number of items in the weighted average,

Answer 23

we can calculate the weighted average of the two data points

i. e: If the average grade of x students in a particular class is 90, what is the average grade received by the left handed students?
- > There are x/5 right handed students in the class; together, they receive an average score of 95.

Question 24

Sets with an odd number of terms -> way to find the position of the median

Answer 24

(n+1)/2

Question 25

Sets with an even number of terms -> way to find the position of the median

Answer 25

between:

n/2 and (n+2)/2

Question 26

When we have evenly spaced set of numbers

Answer 26

the mean and median are equal

What are the mean and median of the first 12 positive multiple of 4
(High+Low)/2= (48+4)/2= 26
** So the mean and median is 26

Question 27

Is it possible to find median even if you have unknown numbers

Answer 27

yes (not 100% of the time though)

Question 28

Mode

Answer 28

Number that appears most in a data set

• > If you see one number occurring more than other one then that can be a mode
• > there can be more than one mode or sometimes no mode

Question 29

Range

Answer 29

Highest Number in a Set- Lowest Number in a Set

Question 30

Standard deviation

Answer 30

measures “how far” a set of values from the average of that set

• > High standard dev= most points in a data set are far from the mean
• > Low standard deviation= most of the data sets are close to the mean
• > Of all the values in the data set are same = standard dev is 0

Question 31

Example of standard deviation

Answer 31

If the stock’s return were one standard deviation of 10 percent. If the stock’s return were -> one standard deviation then it would be [(50-10), (50+10)] = (40,60)
-> two standard deviation then it would be [(50- 210), (50+210)] = (30,70)

Question 32

Standard deviation formula for range

Answer 32

High value = mean+ x(sd)

Low value = mean-x(sd)

Question 33

Does adding or subtracting the same value to all terms does not change the standard deviation

Answer 33

No

i.e
A= {12, 15, 20, 21, 10}
B= {12+x, 15+x, 20+x, 21+x, 10+x}
-> If Set a has a standard deviation of n, then B also has standard deviation of n

Question 34

Does Multiplying or dividing the data set by the same factor does change the standard deviation

Answer 34

not really, it be multiplied or divided by the same amount

-> b/c you are changing it by a constant factor

Question 35

Compare the standard deviation of data set that have an equal number of data points

Answer 35

1) Determine the mean of each set
2) For each individual set, determine the absolute difference between the mean of that set and each data point in that set
3) Sum the absolute difference obtained from each individual set

• > The set that has the largest sum has greatest standard deviation
• > The set that has the smallest sum has s smallest tandard deviation