Ch. 13 Statistics

Question 1

Average =

Answer 1

Sum of terms / # of terms

Question 2

SUM =

Answer 2

Avg x # of terms

Question 3

Number of consecutive integers formula, inclusive

Answer 3

= Highest Number - Lowest + 1

Question 4

Number of consecutive integers formula, exclusive

Answer 4

= Highest Number - Lowest - 1

Question 5

Number of consecutive integers formula, including one endpoint only

Answer 5

= Highest Number - Lowest

Question 6

of multiples of given number formula

Answer 6

= [(Highest multiple - Lowest multiple) / Given number] + 1

+1 b/c you’re including both endpoints (highest & lowest multiple)

Question 7

The methods for getting average efficiently

Answer 7

Evenly spaced sets ONLY
Midpoint - figure out median position
Bookend - average = (first + last) / 2

Question 8

How would you solve this: what is the sum of odd integers from 5 to 55, inclusive?

Answer 8

1. Avg = SUM / #, so we know SUM = avg x #
2. Get average of odd integers from 5 to 55. Because it’s evenly spaced, we can do bookend method: (55 + 5) / 2 = 30
3. Get # of terms - we need all ODD integers: (55 - 5)/2 + 1 = 26
4. Plug into formula: SUM = Avg x # = (30)(26) = 780

Question 9

Formula for “how many multiples of 2 or 3 from 1 to 90, inclusive?”

Answer 9

= Multiples of 2 + Multiple of 3 - Multiples of LCM (2,3)
(B/c we want to remove the double counted multiples)

Question 10

What if the question asks for multiples of 2 or 3 but NOT BOTH? What is the formula?

Answer 10

= Multiples of 2 + Multiples of 3 - (2 x Multiples of LCM(2,3))

Question 11

Weighted Avg formula

Answer 11

Same as average = SUM / # of items

When you’re doing weighted avg, think of PER (e.g., “the score PER student”)

Question 12

Median formula

Answer 12

It’s the number in the (n+1)/2 position

Question 13

When is mean = median?

Answer 13

IN evenly spaced sets

Question 14

What is mode?

Answer 14

Number that occurs most frequently

Question 15

What is the mode if each number occurs the same number of times? e.g., S = {1, 1, 2, 2, 4, 4}

Answer 15

There is no mode

Question 16

Can there be more than one mode?

Answer 16

Yes! If two or more numbers occur MORE frequently than others, then all of these numbers are modes

Question 17

Range = ?

Answer 17

Highest - Lowest number in the set

Question 18

What does standard deviation measure?

Answer 18

How far values in the set are from the average/ mean of the set

Question 19

If the mean is 85 and one standard dev is 5, what amount falls within one standard deviation?

Answer 19

85 +/- 5
= 80 to 90

Question 20

What happens to standard deviation if you +/- the same amount to each element in data set?

Answer 20

Std dev remains the same
{500, 700, 650, 900} has same std dev as
{501, 701, 651, 901}

Question 21

What happens to standard deviation if you multiply/divide by the same amount to each element in data set?

Answer 21

The std dev will also be multiplied/ divided by that amount

Question 22

What is the lowest possible standard deviation?

Answer 22

zero

Question 23

When does a set have a standard deviation of 0?

Answer 23

When all the elements in the set have the same value

Question 24

How do you decrease a positive standard deviation?

Answer 24

Add elements to the set that are = to the mean

Question 25

What is the standard deviation of this set: {15, 15, 15}?

Answer 25

0

Question 26

When range = 0, what is the std dev?

Answer 26

Also 0, because when range = 0, highest = lowest = mean, all the elements in the set are the same value

Question 27

When the highest value = mean, what is the std deviation?

Answer 27

This means all values in the set are the same (otherwise highest or lowest cannot equal mean), so std dev = 0

Question 28

If the range is not 0, can the std dev be 0?

Answer 28

No. If range is not 0, if largest does not equal smallest, then the elements of the set are NOT the same, and std dev cannot be 0. Std dev is GREATER than 0.