Statistics and inferences review - bootcamp

Statistics and Inferences

Review

•Get out two sheets of paper

•Name, date, period on the top

right corner of you paper.

1. Put the data set in order and find

the median and the mean of the

data set.

30, 15, 27, 16, 42

2. Find 5 number summary of the

data set (same data set)

30, 15, 27, 16, 42

Min

(Smallest)

Lower Quartile (Q1)

Median (Q2)

Upper Quartile (Q3)

Maximum (Largest)

3. Make a box and Whisker Plot

with your 5 number summary.

• Remember, your number line needs to go

from the minimum to the maximum, using

a steady interval.

4. Does this data set have an

outlier?

5. What is the best measure to use

for this set of data? Why?

Let’s Check

Put your pencil to the side

Get our your marker or red pen.

Go over your answers.

If it was incorrect, mark it wrong and make corrections in pen or marker.

1. Put the data set in order and find

the median and the mean of the

data set.30, 15, 27, 16, 42

15, 16, 27, 30, 42

Median = 27

Mean = 36

2. Find 5 number summary of the

data set (same data set)

30, 15, 27, 16, 42Min (Smallest) 15Lower Quartile (Q1) 15.5

Median (Q2) 27

Upper Quartile (Q3) 36

Maximum (Largest) 42

3. Make a box and Whisker Plot

with your 5 number summary.

• Remember, your number line needs to go

from the minimum to the maximum, using

a steady interval.

4. Does this data set have an

outlier?

No, no outlier

5. What is the best measure to use

for this set of data? Why?

Mean should be used because

there isn’t an outlier.

Put your marker away, and let’s

practice some more!

6. What is central tendency or

measure of center?

7. What is mean?

How do you find it?

8.What is the

median? How do you

find it?

9. What do you find the median of a

data set if there are more than one

number in the middle of the data

set?2 5 6 12 15 18

10. What is the mode?

11. Which measure of

central tendency is

affected by outliers?

12. What affect will an

extremely small outlier have

on a set of data?

Hint: For example, if you have a really low test grade, how will this affect the mean and median for the set of data?

13. How will really large outliers

affect the mean and median of a

set of data?

Let’s Check





6. What is central tendency or

measure of center?

• It refers to the middle or center of the data.

7.What is mean?

How do you find it?

• It is called the average.

• You add up all the numbers to find a sum.

• You divide the sum by the total numbers in

the data set.

8. What is the median? How do you

find it?

• It is the middle of the data.

• You put the numbers in order and

eliminate one on each side of the data

until you find the middle.

9. What do you find the median of a

data set if there are more than one

number in the middle of the data

set?2 5 6 12 15 18

Find the mean of those two numbers by adding them up and dividing by two.

6 + 12 = 1818/2 = 9The median would be 9

10.What is the mode?

• The number that occurs most often in a

data set.

• 1,2,2,2,3,5,6,7

• The mode would be 2, because it occurs

the most often.

• Some data sets don’t have a more, while

some may have more than one.

11. Which measure of central

tendency is affected by outliers?

Hint: If you made a really low grade, what is

going to affected the most? (Mean or

Median)

The mean is affected by outliers. The mean

of the test scores will go down.

The median is not affected by outliers?

12. What affect will an extremely small

outlier have on a set of data?

Hint: For example, if you have a really low test grade, how

will this affect the mean and median for the set of data?

The small outlier will bring down the

mean (average).

The median will not really be affected.

13. How will really large outliers affect

the mean and median of a set of data?

• The large outlier will cause the mean

(average) to increase.

• It will not really affect the median.


practice some more!

14. Which measure of central tendency

should we use for this data set? Why?


should be used to describe this data set?

16. This line plot has an outlier. Which

measure of central tendency best

describes the data?



18. Find the mean of the data

set

You can find the sum of each line of

numbers

For example:

2 Occurs 5 times, so 2X5

= 10

(24 total pieces

of data)

10

19. Create a line plot with the data.

• 2, 3, 3, 6, 6, 6, 6, 8, 9, 10, 10,

14

20. Find the median of the line plot

you just created.

• ** Use the line plot to find the median.

• Eliminate one on each side until you reach the middle.

Remember to start at the top of each row.

21. Which measure of center

should we use for this line plot?

Let’s Check






should we use for this data set? Why?

This data set has an outlier, so the median

should be used for this data set.



The mean because it data set does not have an outlier.

16. This line plot has an outlier. Which

measure of central tendency best

describes the data?The median because there is an outlier in the

data set.



The median should be used because the data

set has an outlier.

18. Find the mean of the data

set

3 + 10 + 18+16+15+12 + 10

You can find the sum of each line of

numbers

For example:

2 Occurs 5 times, so 2X5

= 10

= 84

---------- = 3.5

24(24 total pieces of data –

count the number of Xs)

19. Create a line plot with the data.

• 2, 3, 3, 6, 6, 6, 6, 8, 9, 10, 10,

14

20. Find the median of the line plot

you just created.

The median is in

between 6 and 6, so

it’s 6

21. Which measure of center

should we use for this line plot?

• The data is spread out. We should use

mean, because there aren’t any outliers.


practice some more!

21.Find the Range of the Box and Whiskers

Plot

Max – min = range

22. Find the Interquartile Range of the B&W Plot

UQ – LQ = IQR

Use the box-and-whisker plots below to answer each question.

23.

Course 2

7-5 Box-and-Whisker Plots

Which set of heights of players has a greater median?

64 66 68 70 72 74 76 78 80 82 84 86 t Heights of Basketball and Baseball Players (in.)

Basketball Players

Baseball Players


24.

Course 2


Which shoe store has a greater median?

20 24 26 28 30 32 34 36 38 40 42 44 t Number of Shoes Sold in One Week at Each Store

Maroon’s Shoe Store

Sage’s Shoe Store

25.What is the range of the box known

as?


26.

Course 2


Which shoe store has a greater interquartile range?



Sage’s Shoe Store

27.

Course 2


Which team is more consistent? Why?


Basketball Players

Baseball Players

28. Fill in the sentence..

• The smaller the Interquartile Range, the

more ______________ the data.


• The higher the Interquartile Range, the

more ______________ the data.

Let’s Check





21. Find the Range of the Box and

Whiskers Plot

Max – min = range

100 – 20 = 80

22. Find the Interquartile Range of the B&W Plot

UQ – LQ = IQR

87 – 50 = 37


23.

Course 2


Which set of heights of players has a greater median?

The Basketball Players


Basketball Players

Baseball Players


24.

Course 2


Which shoe store has a greater median?

Sage’s Shoe Store



Sage’s Shoe Store

25.What is the range of the box known

as?

• Interquartile range


26.

Course 2


Which shoe store has a greater interquartilerange?

Maroon’s shoe store has a longer box, so it has a greater interquartile range.



Sage’s Shoe Store

27.

Course 2


Which team is more consistent? Why?

The Baseball players because they have a smaller range and interquartile range .


Basketball Players

Baseball Players


• The smaller the Interquartile Range, the

more Consistent the data.


• The higher the Interquartile Range, the

more inconsistent the data.


practice some more!

The following slides are a review about

how to find the MAD

(mean absolute deviation).

Just read them and refresh your

memory..

You don’t have to take notes.

Mean Absolute DeviationAnother way to evaluate consistency in

data

Random Survey

• Find the mean of the

data set

The mean is 56

Mean Absolute Deviation

How far away are each piece

of data from the mean?

The mean is 56

• How far is 52 from the mean?



• Find the distance between every piece of data and the mean

Find out how far away each data

set is from the mean.

56

-

56

-

-56

56

-

-56

56

-

- 56 - 56

Now find the average or mean of these

numbers:

4 + 8 + 4 + 1 + 3 + 2 +2 +6

8

4 8 4 1 3 2 2

6

Mean Absolute Deviation

Now find the average or mean of these

numbers:

4 + 8 + 4 + 1 + 3 + 2 +2 +6

8

• = 3.75

• The average distance between each data

value and the mean is 3.75 phone

contacts.

30. Find the Mean Absolute

Deviation for the following data set.

Set A: 1, 10, 7, 6, 4, 8

Steps:

1. Find the mean

2. Find the distance that each value is

away from the mean.

3. Average all the distances.



Set B: 10, 9, 3, 8, 10

Steps:

1. Find the mean

2. Find the distance that each value is

away from the mean.

3. Average all the distances.

32. Which data set is more

consistent, data set A or data set B

(#30 and 31)

Let’s Check







Set A: 1, 10, 7, 6, 4, 8

Mean = 6

5+4+1+0+2+2 = 2.33 = MAD

6

5 4 1 0 2

2

Differences

between each data

set and the mean



Set B: 10, 9, 3, 8, 10

Mean = 8

2+1+5+0+2 = 2 = MAD

5

Differences

between each data

set and the mean

2 1 5 0 2

32. Which data set is more

consistent, data set A or data set B

(#30 and 31)

MAD for Set A = 2.33

MAD for Set B = 2

Data Set B because the MAD is lower.

The lower the MAD, the more consistent the data.


practice some more!

•The next few slides

are review and you

don’t need to take

notes.

Sample is a small group of the

total population

•For a random sample,

members of the population

are chosen at random. This

gives every member of the

population an equal chance

of being chosen.

CONVENIENCE SAMPLE

•A convenience sample is

based on members of the

population that are

conveniently available, such as

30 elk in a wildlife preservation

area.

•A biased sample does not

fairly represent the

population.

• A study of 50 elk belonging to a

breeder could be biased because the

breeder’s elk might be less likely to

have Mad Elk Disease than elk in the

wild.

Which would be better to

have, a random sample or

a convenience sample?

Which would be better to have, a random sample or a convenience sample?

A random sample is more likely to be representative of

a population than a convenience sample is.

The next few slides are questions

that you will answer on your

paper.

Sampling method

Maria surveys only the band students she knows personally.

Results

84% want blue uniforms

Jon writes each band student’s name on a card. He questions those students whose name he draws.


33. Write down the person’s name and determine what

type of sample they took.

Justify your answer.

Sampling method

Ferdinand surveys every other swimmer on the team.

Results

72% want practice early

Anna-Maria questions the swimmers who are in her Biology class.


34. Write down the person’s name and determine what type

of sample they took.


35. If I wanted to find out what people’s

favorite clothing stores was and I stood

outside American Eagle at the mall, what

kind of sample would I be taking?

Would this be a biased sample?

Using a fair, 6 sided di36. What’s the probability of rolling a 5?

37. What’s the probability of rolling a zero?

Using two fair dice

38. What’s the probability that I will roll a

sum of 6?

39.What’s the probability of rolling a sum of

9?

• You can create a sample space to find all the possible combinations.

40.Kenny is playing basketball. He scores 11

out of 34 baskets. What is the probability

that he will make the next shot?

• (Write the fraction, decimal, and percent)

41. The probability of drawing a green

marble is 6/20. What is the probability of

not drawing a green marble?

Let’s Check





Sampling method

Maria surveys only the band students she knows personally.

Results


Jon writes each band student’s name on a card. He questions those students whose name he draws.


33. Write down the person’s name and determine what

type of sample they took.


Maria’s sample is a convenience sample – she sampled only people she knew

Jon’s sample is a random sample, because everyone has the chance of being chosen for the survey.

34. Write down the person’s name and determine what type

of sample they took.

Justify your answer.Sampling method

Ferdinand surveys every other swimmer on the team.

Results


Anna-Maria questions the swimmers who are in her Biology class.


Ferdinand’s sample is a random sample, giving results that better represent the entire swimming team, so it is the better method.

35. If I wanted to find out what people’s

favorite clothing stores was and I stood

outside American Eagle at the mall, what

kind of sample would I be taking?

Would this be a biased sample?

• Convenience sample

• Biased sample

Using a fair, 6 sided di36. What’s the probability of rolling a 5?

1/6 .166 16.6%

37. What’s the probability of rolling a zero?

0/6 0%

38. What is the probability that you

roll the sum of 6?1 2 3 4 5 6

1 1,

1

2,

1

3,

1

4,

1

5,

1

6,

1

2 1,

2

2,

2

3,

2

4,

2

5,

2

6,

2

3 1,

3

2,

3

3,

3

4,

3

5,

3

6,

3

4 1,

4

2,

4

3,

4

4,

4

5,

4

6,

4

5 1,

5

2,

5

3,

5

4,

5

5,

5

6,

5

6 1,

6

2,

6

3,

6

4,

6

5,

6

6,

6

# outcomes that equal 6

Total # outcomes

5

36 =13.9%

39. What is the probability that you

roll the sum of 9?1 2 3 4 5 6

1 1,

1

2,

1

3,

1

4,

1

5,

1

6,

1

2 1,

2

2,

2

3,

2

4,

2

5,

2

6,

2

3 1,

3

2,

3

3,

3

4,

3

5,

3

6,

3

4 1,

4

2,

4

3,

4

4,

4

5,

4

6,

4

5 1,

5

2,

5

3,

5

4,

5

5,

5

6,

5

6 1,

6

2,

6

3,

6

4,

6

5,

6

6,

6

# outcomes that equal 9

Total # outcomes

4

36 =1

9

11.11%

40.Kenny is playing basketball. He scores 11

out of 34 baskets. What is the probability

that he will make the next shot?

11/34 = .3235 = 32% chance he makes the

shot

• (Write the fraction, decimal, and percent)

41. The probability of drawing a green

marble is 6/20. What is the probability of

not drawing a green marble?

14/20 = .7 = 70%

Statistics and inferences review - bootcamp

Education