Statistics and formula logic

Question 1

Average =

Answer 1

Sum / #

Question 2

How do you find the number of terms in a set of consecutive integers that only includes one of its endpoints but not both?

Answer 2

Last # - first #

Question 3

How do you find the # of terms between two numbers in a set of consecutive integers?

Answer 3

Last # - first # - 1

Question 4

What is an evenly spaced set?

Answer 4

The numbers in the set increase or decrease by the same amount (and therefore share a common difference)

Question 5

How to count the # of consecutive integers in a set that includes the first and last numbers?

Answer 5

Highest # - lowest # +1

Question 6

How to count the # of consecutive multiples of a given # in a range of values that are inclusive of the first and last numbers?

Answer 6

((Highest # divisible by the given # - lowest # divisible by the given #)/ given #) + 1

Question 7

How do you determine the average of an evenly spaced set of terms?

Answer 7

(First term + last term) / 2

Question 8

What is the average of the terms in an evenly spaced set with an odd # of terms?

Answer 8

The middle term when the terms are in numerical order.

Question 9

What is the average of the terms in an evenly spaced set with an even # of terms?

Answer 9

The average of the two middle terms of the set when the terms are in numerical order.

Question 10

How to count the # of consecutive multiples of two given #s in a range of values that are inclusive of the first and last numbers?

Answer 10

Don’t want to double count ***

The # of multiples of A or B =
The # of multiples of A + the # of multiples of B - the # of multiples of LCM(A,B)

Question 11

How to count the # of consecutive multiples of two given #s (but not of both) in a range of values that are inclusive of the first and last numbers?

Answer 11

The # of multiples of A or B =

The # of multiples of A + the # of multiples of B - 2*(the # of multiples of LCM(A,B))

Question 12

What is the weighted average formula?

…Expanded?

Answer 12

Weighted Avg = sum of weighted terms / total number of weighted terms

(Data point 1)(frequency of data point 1) + (data point 2)(frequency of data point 2) … (data point n)(frequency of data point n) / (total frequency of data points)

Question 13

In an evenly spaced deck, the mean is equal to what?

Answer 13

The median

Question 14

S={1,4,6,7,4,8,7,7,4}

What is the mode of S?

Answer 14

4 and 7

Question 15

S={1,4,6,7,3,8,5,9,2}

What is the mode of S?

Answer 15

No mode

Question 16

S={1,4,6,7,6,4,1,7}

What is the mode of S?

Answer 16

No mode

Question 17

Range =

Answer 17

Highest number in a set - lowest number in a set

Question 18

What does it mean when the standard deviation is 0?

Answer 18

All the values in the data set are the same (no difference between and of the terms and the mean)

Question 19

What does standard deviation measure?

Answer 19

How far a set of values are from the average of that set

Question 20

What is the standard deviation formula?

Answer 20

High value = mean + x(SD)

Low value = mean - x(SD)

Question 21

When you add or subtract the same amount from each term in a data set, what happens to the standard deviation?

Answer 21

It stays the same

Question 22

If all the terms in the set are the same, what is the standard deviation?

Answer 22

0

Question 23

What happens when you multiply or divide the elements of a data set by a constant amount?

Answer 23

The standard deviation will also be multiplied/divided by that amount

Question 24

What is the least possible standard deviation of a set?

Answer 24

0

Question 25

What is one way to guarantee that a positive standard deviation in a set will decrease.

Answer 25

Add elements equal to the mean.

Question 26

How do you know which set has the bigger standard deviation?

Answer 26

1. Find the avg of each set
2. Find the absolute difference of each term in the set from the average of that set and sum these absolute differences up.
3. The highest sum will have the highest standard deviation.

Question 27

How do you determine the factor by which a formula changes if one of the terms changes?

Answer 27

New formula / old formula

Question 28

When the largest value in a set is equal to the smallest value, what is the range and standard deviation?

Answer 28

Both 0

Question 29

If we are given that either the largest value or the smallest value in a data set is equal to the mean, what does this mean about all the data points in the set and the standard deviation of that set?

Answer 29

all the data points in the set are the same and the standard deviation is 0