Histograms: Use quantitative Data

1. Create a scale for your x axis2. Figure out where your data fits into your

scale3. Figure out a scale for your y axis4. draw in your barsDon’t forget a title/label your axes

Like bar graphs but for quantitative data. All bars connected

Step 1.

Here is a set of data stating the inches of rain received in the month of March in Tacoma, Washington in 2008 unit is in inches

3, 6, 0, 9, 3.5, 2.7, 6.1, 3.4, 5.6, 2.9, 3.4, 7.8, 0, 0, 0, 7, 2.9, 4.5, 7.9, 3.4, 2.1, 3.2, 3.6, 5.6, 5, 8, 0, 1, 3.6, 9, 0

Data has a small spread (low zero high is 9 so probably want to go by a small number, you should have at least 5 bars I will go by 2’s

Step 2: Place your data

3, 6, 0, 9, 3.5, 2.7, 6.1, 3.4, 5.6, 2.9, 3.4, 7.8, 0, 0, 0, 7, 2.9, 4.5, 7.9, 3.4, 2.1, 3.2, 3.6, 5.6, 5, 8, 0, 1, 3.6, 9, 0

# range Amount of numbers that fit into these spots

0-1.999 bar 1

2-3.999 bar 2

4-5.99 bar 3

6- 7.99 bar 4

8-9.99 bar 5

Step 2: Place your data

# range Amount of numbers that fit into these spots

0-1.999 (bar 1) 7

2-3.999 Bar 2 12

4-5.99 Bar 3 4

6- 7.99 Bar 4 5

8-9.99 Bar 5 3

3, 6, 0, 9, 3.5, 2.7, 6.1, 3.4, 5.6, 2.9, 3.4, 7.8, 0, 0, 0, 7, 2.9, 4.5, 7.9, 3.4, 2.1, 3.2, 3.6, 5.6, 5, 8, 0, 1, 3.6, 9, 0

Step 3: Y axis scale

There are only 31 points, so going by a small scale would be better

I will go by 2’s

The more data points the larger the scale

4. Making the Histogram

2 4 6 8 10 12Inches of rain

14

12

10

8

6

4

2

Rain in March (inches)

# of days

Shape Part 1: Mode Shape Part 2: Skew

Unimodal, bimodal, and multimodal Unimodal: one high bar?

Bi Modal: two high bars that are about the same?

Multimodal: three bars that are about the same height

Skew right, left, or uniform, centered Skew Right: tail goes to higher

numbers

Skew Left: Tail goes to lower Numbers

Uniform: all bars about the same length

5. Describe The Distribution for all histograms, you must describe shape, center, spread, and whether there are gaps and

outliers

Center: Where are the highest bars

State where the highest bars are and DON’T FORGET TO INCLUDE YOUR UNITS!!!!

List them all

Spread

Loose: large range of numbers on x axisTight: a small range of numbers on x axis

Gaps: Where are there holes? List them all

Where are your outliers? List them all

Don’t forget your units Gaps: a hole where there

are not any bars.

Example: there is a gap from 2 to 4 ft

5. Describe The Distribution for all histograms, you must describe shape, center, spread, and whether there are gaps and

outliers

A gap

Don’t forget your units

Example: there is an outlier from 4-6 feet

(for histograms a range)

Always isolated(maybe only one or two by each other

An outlier

5. What,s the distribution

2 4 6 8 10 12Inches of rain

14

12

10

8

6

4

2

Rain in March (inches)

# of days

5. Describing shape center, spread and outliers

Shape: unimodal one peak, skew right

Center: Center is at 2-4 inches of rain, Spread: Spread tight

Gaps and outliers: no gaps and no outliers

For the following data make a histogram and describe the shape, center, spread gaps and outliers

Hrs. of sleep over a three week period for Mrs. Chambers

6, 8, 5, 4, 6, 8, 7, 8, 8.5, 9, 5, 7, 8, 7.5, 6, 5, 6.5, 3, 7.5, 8, 8.5

Everyone make their own to get the assignment

Don’t forget, at least 5 bars

Do now 10/5

Describe the distribution using complete sentences for the following histogram

8 10 12 14 16Hours of time awake

654321

# of people

Hrs. of time awake for people age 20-35

Quiz on histograms

For the following set of data, create a histogram and then describe the distribution

# of frogs seen in lake Wapato over a two week period

35, 21, 4, 11, 23, 16, 22, 18, 13, 6, 7, 20, 17, 17,

Stem and Leaf Plots

1. Find the range of your stem (lower numbers on bottom)

2. Organize your data points (leaves)3. Make your stem and leaf plot4. Describe the distributionDon’t forget your labels and the title

Step 1. Determine the range of your stem

Copy down this data

# of pennies found on the ground at Mt. Tahoma in the month of June 5, 0, 9, 6, 8, 12, 15, 0, 9, 7, 11, 13, 32, 6, 6, 4, 2, 7, 9, 5,

6, 7, 0, 1, 9, 13, 16, 7, 9, 4

Find your highest and lowest point

If your data has decimals then your stem is the whole numbers

If your data had whole numbers then your stem is the tens (0, 10’s, 20’s, 30’s etc)

2. Now place leaves (data points) on the stem

Organize your data:

Determine if you need to divide your stem (have two sections for each stem because you have a lot of data in one section (For example in this problem we have a lot of single digit #’s

Range # of days

0-9 23

10-19 6

20-29 0

30-39 1

3. Create your stem and leaf Plot

Create your stem (2 for each number because so much data)

Place leaves

Make sure data points are from smallest to largest

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15-1910-145-90-4

Stem

00

1

3. Create your stem and leaf Plot

Don’t forget the Title and make sure you have all 30 points!

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Stem

2

56123355666677778999990001244

Pennies found on the ground in June

4. Describe your distribution

Don’t forget the Title and make sure you have all 30 points!

33221100

Stem

2

56123355666677778999990001244

Pennies found on the ground in June

Shape: Skew to higher numbers Or skew to lower numbers

Mode: how many peaks

Center: Where are all the longest sections

Spread: (always tight for stem and leaf or else too much data)

Gaps and OutliersList all outliers even if numbers repeat

Individual assignment

Make the following 2 stem and leaf plots and describe the distribution. Don’t forget a title and a key for each one

Data set 1: # of M&M’s in a two pound bag 223, 184, 265, 255, 254, 265, 275, 289,

253, 265, 248, 265, 235, 265, 278, 256

Data set 2: miles I walked in a two week period3.2, 1, .5, 3.4, 5, 1, 2, 3.2, 5, 1.2, 2.4,

3.5, 1.8, 2.7

Back To Back stem and Leaf

1. Find high point and low point of data look in both lists

2. Make your stem3. Plot one set of data on one side of stem

and one set of data on the other side of the stem

4. Describe the distributions of both sides separately

5. Don’t forget titles!

1. Find high and low in data

Copy down the data and then find your high and low points

# of pieces of candy each house gave trick or treating on Alder street: 12, 10, 9, 8, 2, 1, 0, 30, 9, 12

# of pieces of candy I got trick or treating on Lawrence street: 30, 31, 20, 25, 6, 27, 0, 26, 9, 26, 33, 40

2/3: Make stem and plot data

Don’t forget Titles and make sure you have all points for both sides!

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001305667

069

Lawrence Street CandyAlder St. Candy

0

220998210

2/3: Make stem and plot data

Don’t forget Titles and make sure you have all points for both sides!

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Lawrence Street CandyAlder St. Candy

4: Describe Distribution

Don’t forget Titles and make sure you have all points for both sides!

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001305667

069

Lawrence Street CandyAlder St. Candy

0

220998210

Alder St. Distribution:Shape: unimodal, skew upCenter: 0-9 pieces of candySpread: TightGaps: 20-29 pieces of candyOutliers: 30 pieces of candy

Lawrence St. Distribution:Shape: unimodal, skew upCenter: 20-27 pieces of candySpread: TightGaps: 10-19 pieces of candyOutliers: 0,6,and 9 pieces of candy

Do now: Make a back to back stem and leaf plot

# of fish in Wapato: 10, 20, 30,56, 45, 32, 80, 35, 36, 46, 78

# of fish in lake Tahoma: 23,56, 78, 65, 45, 89, 46, 23, 11, 89, 56, 78, 23, 0, 65

Quiz: stem and leaf plot make them and describe the distributions

# of students absent of Fridays in statistics second semester in 2011 3, 0, 5, 2, 3, 4, 2, 3, 6, 7, 15, 0, 1, 3, 4, 5, 7, 9, 3, 3, 2, 7, 1, 0,

0, 5, 8, 9, 15

Now make a back to back stem and leaf plot using the data above and this data then compare their distributions

# of students absent from Algebra on Fridays in 2011

6, 7, 8, 2, 3, 5, 6, 7, 8, 4, 8, 7, 6,9, 12, 13, 5, 6, 4, 3, 4,5,

Dot plots

Copy down the data

For the following set of data, create a dot plot

# of skittles eaten in a day40, 41, 35, 41, 43, 44, 45, 47, 48, 47, 47, 48,

45, 41, 45, 50, 48, 47, 47, 45, 45, 47, 44, 41, 42, 43, 44, 45

Dot plots

# of skittles eaten in a day40, 41, 35, 41, 43, 44, 42, 47, 48, 47, 47, 48,

45, 46, 45, 50, 48, 47, 47, 45, 40, 47, 44, 46, 42, 43, 44, 45

Dot plots describe distributions

Shape skew left, unimodal at 47 skittles (6 times)Tight spreadGap from 26-39 skittles and 49 skittlesOutlier: 35 skittles

# of skittles eaten in a day

Dot plot reminders

Scale must go by 1Don’t forget the titleDon’t forget to list how many dots are at the

mode

Time Plot

Copy down the following set of data and notes

Year # of A’s in classes

1990 6

1991 4

1992 3

1993 5

1994 5

1995 6

1996 6

1997 2

1998 6

1999 6

Time plots have years on the x axis

On y axis is right hand column

All dots are connected by a line

Time Plot

You try

Make a dot plot and describe distribution # of A’s on tests: 15, 16, 17, 16, 15, 5, 7, 8, 7, 8, 6, 5,

4, 16, 15, 15, 10, 11, 12, 13, 13, 15, 15

Make a time plot, give max/min and where most data is

Yr Touchdown’s scored

1956 2

1957 0

1958 8

1959 7

1960 7

Things to remember for assignment on time and dot plots

1. your are making a time plot and a dot plot for mean age

2. don’t forget to describe distribution for all dot and time plots

3. don’t forget to do the back of the worksheet

4. don’t forget your units

Dot plot: Make a dot plot and describe the distributions

Time plot; make a time plot and give max, min, and most common

Ounces of water I drink in a day

50, 49, 58, 45, 52, 52, 51, 58, 56, 57, 62, 58, 59, 50, 58, 57, 58, 56, 56, 52, 51, 58, 58, 52, 50, 51, 49

Month Inches flower grew

December .5

January .2

February .3

March .7

April .8

May 1.0

June .7

July .6

August .4

Quiz dot and time plot