histograms & summary data. summarizing large of amounts of data in two ways: histograms: graphs...
Post on 20-Dec-2015
218 Views
Preview:
TRANSCRIPT
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 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
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”
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
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”
Histograms & Summary Data
What is the smallest height?
Answer: 67 inches
What is the largest height?
Answer: 91 inches
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
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
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
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
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
Histograms & Summary Data
Using NBAPlayerHeights.xls, create a histogram with bin widths of 5 starting at 65 inches
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.
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
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
Histograms & Summary Data
Plotting
Choose “Columns”
Cell Range of your Histograms Frequencies goes here
Click “Next”
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”
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)
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.
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
10
20
30
40
50
60
70
80
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140
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
50
60
70
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
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
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
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
.
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
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
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
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
.
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
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
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
.
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)
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)
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
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
top related