Word Problems: Statistics & Consecutive Sets

Question 1

What is the range?

Answer 1

Difference between biggest number and smallest number in a set

Question 2

What is an average?

Answer 2

Avg is the sum of a set divided by the number of terms in the set.

Question 3

What is the median?

Answer 3

It is the number in the middle of a set. If the set has an even about of terms, then the median is the avg of the two middle numbers

Question 4

What is the standard deviation?

Answer 4

It is the “spread” of the set or variety. Indicates how far from the avg the data points typically fall.

Think: If I put this number set on a number line, how far would it spread?

A small sd: means # are closer to avg.

A large SD: set is spread out widely

Question 5

What two things should you do for EVERY statistics problem?

Answer 5

Visualize it and write it down!

Commit or get out quick!

Question 6

What is the avg in a consecutive (eg evenly spaced) set? Why is that important?

PS180-OG 16
PS90 OG15

Answer 6

The average is the median. This means that you can find the sum of the consecutive set. Each concentric pair will have the same sum, we just need to know how many pairs there are so we know how many sums make up the total sum. And you can find the number of pairs by dividing the number of terms by 2.

Question 7

What are two ways to use avgs to find the sum of a big consecutive set?

Answer 7

Use a menorah and pair up the concentric pairs

know that avg= sum/# terms and avg=median
median= Sum of pairs/2
Set avg=median
sum/#terms = Sum of pairs/2

Question 8

What is a weighted avg and how is it different from regular avg?

Answer 8

Weighted avgs help in finding the combined avg for different groups.

Calculating a regular avg between the group can only be calculated when the two groups have the same amount of terms.

A weighted avg is used when this is not the case.

Question 9

How do you solve a weighted avg problem?

Answer 9

Draw a scale between the two avgs of the groups. If the overall avg is given, place it on the scale. Whichever group it is closest too will be larger (eg have more terms).

Draw a scale, and put the extremes of the two groups at either end: eg 100% of x at one end and 100% of y at the other end. Then in the middle, calculate what it would be if there was a 50/50 split between the two, state where the actual amount is. the end it’s closest to has more in the mix.

Question 10

What is a signal word for weighted avg?

Answer 10

Mixture

Question 11

How do you use algebra for a weighted avg problem?

PS 131 Q1

Answer 11

1. Draw a table with each piece of the mixture on the top: eg Food X +Food Y =Mixture (total)
   - Draw the rows to reflect what is in the mixture and total: eg Protein + Other=total
2. Fill in the chart with what you know.
3. Use equations to solve for a variable, plug in to find the right variable.

Question 12

Diamond X strategy

Answer 12

Look back at notes

Question 13

What is this question implying:

“the cost per employee, if equally shared, is $20”

Answer 13

The avg is $20

Question 14

What is this question implying:

“per capita income”

Answer 14

The average income per person in an area

Question 15

How would you solve:

Sam earned a $2k commission on a big sale, raising his avg commission by $100. Is Sam’s new average commission is $900, how many sales has he made?

Answer 15

Set up an avg formula table and solve for n.

n=11

Question 16

How do you find a median in a set that contains an unknown?

Answer 16

The median only depends on two numbers in the set. So, sometimes you can find it even if the set has an unknown value. However, sometimes you will need to know the value.

(x,2,5,11,11,12,33) = median will always be 11.

Question 17

If each data point in a set is increased by a factor of 7, does the set’s SD increase, decrease or remain constant?

Answer 17

SD will increase. It will make all gaps between points 7 times as big as they originally were. SD will increase by a factor of 7

Question 18

How do you calculate the standard deviation?

Answer 18

1. Find the average of the set.
2. Find the absolute differences of each term and the avg number.
3. Take the avg of those differences. This is the spread (which gives to moderate (2), or large (5) SD)

Question 19

What is a consecutive set?

Answer 19

A set of numbers that follow one after the other without skipping any integers. You can have a consecutive even integer set and consecutive prime set

Question 20

What is an evenly spaced set?

Answer 20

A set of numbers that go up or down by the same amount (increment): 2,5,8, 11, 14 have an increment of 3.

-Evenly spaced sets (Constant increments)

Question 21

What is a set of consecutive multiples

Answer 21

special case of evenly spaced set. All of the values are multiples of the increment (12, 16, 20, 24) Must be composed of integers.

Within Evenly spaced sets circle, the consecutive multiples are multiples of the increments.

Question 22

What are consecutive integers?

Answer 22

special case of consecutive multiples: all the values increase by 1. And are multiples of 1.

Within the consecutive multiples circle, consecutive integers are in increments of 1.

Question 23

How do you find out how many terms are in a consecutive integer set? For example, the range of 4-10

Answer 23

Last-First +1

10-4+1=7

Question 24

How do you find out how many terms are in a consecutive multiple set? For example, the range of even set 2-50?

Answer 24

(Last-First)/multiple +1

50-2=48/2 =24 +1 =25

Question 25

What are the properties of evenly spaced sets?

Answer 25

1. The arithmetic mean= median

2. The mean and median of the set are equal to the average of the first and last terms.

Question 26

What do you know about the avg of a n odd number of consecutive numbers?

What about the avg of an even number of consecutive integers?

Answer 26

Odd= avg and median is an integer

Even= avg and median are not integers.

Question 27

What is important about divisibility of consecutive integers?

Answer 27

The product of consecutive integers (K) or more, is always divisible by K because the integers are factors of K.

Question 28

What is the equation for the sum of 1 to n consecutive integers?

Answer 28

(n(n+1))/2