Histograms & Summary Data

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Histograms & Summary Data

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Histograms & Summary Data. Histograms & Summary Data. Summarizing large of amounts of data in two ways: Histograms: graphs give a pictorial representation of the data Numerical summaries: gives snapshot of the data overall: “Average”, “Mode”, “Median”, etc. Histograms & Summary Data. - PowerPoint PPT Presentation

Transcript of Histograms & Summary Data

Page 1: Histograms & Summary Data

Histograms & Summary Data

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Histograms & Summary Data

Summarizing large of amounts of data in two ways:

Histograms: graphs give a pictorial representation of the data

Numerical summaries: gives snapshot of the data overall: “Average”, “Mode”, “Median”, etc

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Histograms & Summary Data Microsoft Excel has several tools that allows to

summarize data: sorting Maximum Minimum range (difference between max and min) mean (average) grouping data plotting a histogram

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Histograms & Summary Data

Sorting in Excel

Click on “Data”

Click on “Sort”

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Histograms & Summary Data

Sorting in ExcelStore the data to be sorted in a list by columns

Click to sort the column from low to high and vice versa

Click “OK”

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Histograms & Summary Data

Sorting in Excel

Ex: On the class webpage, go to the file NBAPlayerHeights.xls

File contains data for the top ten player heights (in inches) by team during the 1990-91 season

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Histograms & Summary Data

Use the Sort tool in Excel to list all the player heights from smallest to largest

First, highlight the data you wish to sort

Go to “Data” and click “Sort”

Click “Ascending”, then click “OK”

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Histograms & Summary Data

What is the smallest height?

Answer: 67 inches

What is the largest height?

Answer: 91 inches

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Histograms & Summary Data MIN and MAX functions find the minimum value(s)

and maximum value(s) in a list

The range is the maximum minus the minimum

AVERAGE function finds the average or mean

SUM function adds numbers in a list

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Histograms & Summary Data Excel also has a Histogram tool

This function separates data into bins

The function counts how much data lies within each bin

You can (and should) define the size of the bin prior to opening the function

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Histograms & Summary Data

A histogram organizes data into groups by counting how much data is in each group

The groups are sometimes called “bins”

The number of observations in each “bin” is called the frequency

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Histograms & Summary Data

Installing the Histogram feature:Click on “Tools” and then on “Add-Ins”

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Histograms & Summary Data

Installing the Histogram feature:

Click on these boxes

Hit “OK” to install. It will take a few moments for these packs to install

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Histograms & Summary Data

Creating a Histogram

Click on “Tools”

Click “Data Analysis”

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Histograms & Summary Data

Creating a Histogram

Click on “Histogram”

Click “OK”

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Histograms & Summary Data

Creating a Histogram:Cells where your data is stored goes here

Your Bin Limits or Bin Widths go here. You need to type these beforehand in your worksheet

Choose the cell you want the frequencies of your bins to be displayed in Excel

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Histograms & Summary Data

Using NBAPlayerHeights.xls, create a histogram with bin widths of 5 starting at 65 inches

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Histograms & Summary Data

Create Bin Limits in Excel

Create a cell called “Bin Limits”

Enter your Bin Limits. Since we want bin to be width 5 there is only a difference of 5 between consecutive cells.

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Histograms & Summary Data

Create HistogramCell Range of Data Goes Here

Bin range you created goes here

The cell where you want the frequencies to be displayed

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Histograms & Summary Data

And the Results . . .

This number counts the number of times that player heights were greater than 65 but less than or equal to 70 inches

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Histograms & Summary Data

Plotting Our Results: Click on Chart Wizard

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Histograms & Summary Data

Select Chart Type

Click “Column”

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Histograms & Summary Data

Plotting

Choose “Columns”

Cell Range of your Histograms Frequencies goes here

Click “Next”

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Histograms & Summary Data

Plotting:

Type in the Cell Range of the Bin Limits your created

Click on “Series” tab from previous slide

Click on “Finish”

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Histograms & Summary Data

And the results:

0

20

40

60

80

100

120

140

65 70 75 80 85 90 95

Series1

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Histograms & Summary Data

Ex. Consider Excel file Sick Time.xls Find the mean, max, min, and range of hours at the Central plant.

Soln. Mean: 25.21 hours

Min: 0 hours

Max: 137 hours

Range: 137 hours (max – min)

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Histograms & Summary Data

Ex. Construct a histogram of data with bin sizes of 10 hours. Construct another histogram of data with bin sizes of 8 hours.

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Histograms & Summary Data

Soln. Bin Frequency

0 4910 4220 7030 6040 3150 1060 570 380 490 6100 2110 3120 3130 7140 1

More 0

0

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0 10 20 30 40 50 60 70 80 90 100 110 120 130 140

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Histograms & Summary Data

Soln. Bin Frequency

0 498 2916 6624 4932 4040 1948 956 564 372 280 388 696 2104 2112 2120 2128 5136 2144 1

More 0

0

10

20

30

40

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70

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Histograms & Summary Data

Focus on the Project

In the sheet Data of Queue data.xls we see that the Friday 9 a.m. has more people that all other days at 9 a.m.

There is historical data for 5 weeks

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Histograms & Summary Data

Focus on the Project

A summary of the 9 a.m. data is given in the Excel file

COUNTIF MIN AVERAGE MAX MAX - MIN

Number of Times

Minimum Time

Mean Time

Maximum Time

Range of Times

573 0.00 0.52 3.46 3.46

Times Until and Between Arrivals: 9-10 a.m., Friday

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Histograms & Summary Data

Focus on the Project

Since there are 573 customers in the 5 hours of data, this gives us customers per hour

For 60 minutes in an hour, this means that there are approx. 0.5236 minutes between arrivals

6.1145573

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Histograms & Summary Data

Focus on the Project

Create a histogram of the data, using appropriate bin limits (around 0.2 to 0.3 minutes for bin width) TIMES: 9-10 a.m., FRIDAY

0.00

0.10

0.20

0.30

0.40

0.50

0.15 0.75 1.35 1.95 2.55 3.15times

rel.

freq

.

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Histograms & Summary Data

Focus on the Project

From the histogram, we see that almost half of all the times between arrivals is less than 0.3 minutes

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Histograms & Summary Data

Focus on the Project

A summary of the 9 p.m. data is given in the Excel file

COUNTIF MIN AVERAGE MAX MAX - MIN

Number of Times

Minimum Time

Mean Time

Maximum Time

Range of Times

149 0.02 1.92 10.37 10.35

Times Until and Between Arrivals: 9-10 p.m., Friday

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Histograms & Summary Data

Focus on the Project

Since there are 149 customers in the 5 hours of data, this gives us customers per hour

For 60 minutes in an hour, this means that there are approx. 2.0134 minutes between arrivals

8.295149

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Histograms & Summary Data

Focus on the Project

Create a histogram of the data, using appropriate bin limits (around 1 minute for bin width) TIMES: 9-10 p.m., FRIDAY

0.0

0.1

0.2

0.3

0.4

0.5

0.5 2.5 4.5 6.5 8.5 10.5

times

rel.

freq

.

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Histograms & Summary Data

Focus on the Project

Now that we know arrival time, we shift focus to service times

Service times do not depend upon time of day nor day of week

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Histograms & Summary Data

Focus on the Project

Service times for a single week are given in the file Queue Data.xls

There are 7634 service time records

Create histogram of these records

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Histograms & Summary Data

Focus on the Project

Bin size used – around 0.20WEEK 1 SERVICE TIMES

0.00

0.04

0.08

0.12

0.16

0.20

0.00 0.45 0.99 1.53 2.07 2.61 3.15 3.69 4.23

times

rel.

freq

.

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Histograms & Summary Data Focus on the Project [9 a.m.] Mean (average) arrival time is 0.52 minutes Mean (average) service time is 1.21 minutes

Therefore, 1 ATM is probably not enough (using ONLY the mean times)

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Histograms & Summary Data

Focus on the Project [9 a.m.] If two ATMs were available for two customers, it

would take 1.21 minutes The service time would then be 0.605

Therefore, 2 ATMs are probably not enough (using ONLY the mean times)

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Histograms & Summary Data

Focus on the Project [9 a.m.] By similar reasoning, 3 ATMs should be adequate

(Note: 1.21/3 = 0.403 minutes per customer)

[9 p.m.] 1 ATM would probably be adequate

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Histograms & Summary Data Focus on the Project – What you should do:

Analyze the team data (number, min, mean, max, and range)

Create histograms for 9 a.m. and 9 p.m. arrival times

Create histogram for service times

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Histograms & Summary Data

Focus on the Project – What you should do:

Form preliminary estimates for the number of ATMs required for each of the two hours (9 a.m. and 9 p.m.)