I found the concept on frequency distribution using Google and the search words “frequency distribution” at http://www.mathsisfun.com/data/frequencydistribution.html This website is geared towards younger people and therefore breaks down frequency distribution into very basic terms: values and their frequency (how often each value occurs). The website uses the example of a child’s soccer team and how many goals they scored in recent games. For the assignment this week, I have chosen to use the raw data of shoe sizes of my coworkers and how often these shoe sizes occur and show how to put them into a frequency distribution table. Because there are only 4 females in my division, I have stuck with only the male shoe sizes of 20 coworkers. Raw Data
101291011
81011109
98111010
121091011
Each raw data value is now placed into a class. Since my range of data is small, I’m going to use single data values. Distribution Table
Class LimitsTallyFrequency
8II2
9IIII4
10IIII IIII8
11IIII4
12II2
Total: 20
This can also be done in excel by following the instructions for a categorical frequency table for qualitative or discrete data on page 215 (49) of our textbook. Taking it a step forward, the information can then be used in a pie chart to visually see the frequency of each shoe size.
...Statistics:
• Science of gathering, analyzing, interpreting, and presenting data
• Measurement taken on a sample
• Type of distribution being used to analyze data
Descriptive statistics:
Using data gathered on a group to describe or reach conclusions about that same group only. Descriptive statistics are the tabular, graphical, and numerical methods used to summarize data.
Collect, organize, summarize, display, analyze
Eg: According to Consumer Reports, General Electric washing machine owners reported 9 problems per 100 machines during 2002. The statistic 9 describes the number of problems out of every 100 machines.
Inferential statistics:
Using sample data to reach conclusions about the population from which the sample was taken. Statistical inference is the process of using data obtained from a small group of elements (the sample) to make estimates and test hypotheses about the characteristics of a larger group of elements (the population).
Predict/forecast, make estimates about population behavior based on sample, , test hypothesis, make decisions
Eg 1: TV networks constantly monitor the popularity of their programs by hiring Nielsen and other organizations to sample the preferences of TV viewers.
Eg 2: The accounting department of a large firm will select a sample of the invoices to check for accuracy for all the invoices of the company.
Data:
Data are the facts and figures that are collected, summarized, analyzed, and...
...the iRiver, and the Magic Star MP3. To summarize the consumer responses with a frequency table, how many classes would the frequency table have?
4. Two thousand frequent Midwestern business travelers are asked which Midwest city they prefer: Indianapolis, Saint Louis, Chicago, or Milwaukee. The results were 100 liked Indianapolis best, 450 liked Saint Louis, 1,300 liked Chicago, and the remainder preferred Milwaukee . Develop a frequency table and a relative frequency table to summarize this information.
5. Wellstone, Inc., produces and markets replacement covers for cell phones in a variety of colors. The company would like to allocate its production plans to five different colors: bright white, metallic black, magnetic lime tangerine orange, and fusion red. The company set up a kiosk in the Mall of America for several hours and ask randomly selected people which cover color was their favorite:
Bright white 130
Metallic black 104
Tangerine orange 455
Fusion red 286
A. What is the table called?
B. Draw a bar chart in the table.
C. Draw a pie chart.
D. If Wellstone, Inc., plan to produce million cell phone covers, how many of each color should it produce?
11. Wachesaw Manufacturing, Inc., produced the following number of units in the last 16 days.
27, 27, 27, 28, 27, 25, 25, 28
26, 28, 26, 28, 31, 30, 26, 26
the information is to be organized into a frequency...
...SPSS: Grouped FrequencyDistribution
FIRST STEP: Under the Transform menu, choose Visual Binning… This
command assists you in creating a new variable that groups the data. You
will then use the new variable to create a grouped frequencydistribution.
• From the Variables list box, click on wt (weight) and then on the arrow to
move it to the Variable to Band list box. Click Continue.
• Select wt in the left box. Near the top of this dialog box, enter a name for
your new variable (such as wt_groups) in the “Binned Variable” box
(cannot have any spaces in the name).
• Near the lower right, click Make Cutpoints…
• We are going to make Equal Width Intervals, which is the default selection
in this dialog box. You have to fill in 2 of the 3 fields; for our purposes, fill
in “Number of Cutpoints” and “Width”.
• As discussed above, generally 10 to 15 intervals works well. The Number
of Cutpoints = [number of intervals – 1]. (Why? * ) Thus, if we want 10
intervals, we’ll enter 9 in the “Number of Cutpoints” box.
• For the “Width” of each interval: (a) find the difference between the lowest
and highest score in your data (you can see these values in the
background dialog box behind the active dialog box); (b) divide the
difference by the number of intervals (in this example, [122.7 – 65] / 10 =
5.77); and (c) round up to the whole number (6.0). Enter that number as
the interval Width.
*...
...FREQUENCY POLYGONS
W H AT I S A F R E Q U E N C Y P O LY G O N
Frequency polygons are a graphical device for
understanding the shapes of distributions. They
serve the same purpose as histograms, but are
especially helpful for comparing sets of data.
Frequency polygons are also a good choice for
displaying cumulative frequencydistributions.
H O W T O C R E AT E A F R E Q U E N C Y
P O LY G O N
To create a frequency polygon, start just as for histograms, by
choosing a class interval. Then draw an Xaxis representing the
values of the scores in your data. Mark the middle of each class
interval with a tick mark, and label it with the middle value represented
by the class. Draw the Yaxis to indicate the frequency of each class. Place
a point in the middle of each class interval at the height corresponding to
its frequency. Finally, connect the points. You should include one class
interval below the lowest value in your data and one above the highest
value. The graph will then touch the Xaxis on both sides.
E X A M P L E O F A F R E Q U E N C Y TA B L E
Lower
Limit
Upper
limit
Count
Cumulativ
e
29.5
39.5
0
0
39.5
49.5
3
3
49.5
59.5
10
13
59.5
69.5
53
66
69.5
79.5
107
173
79.5
89.5
147
320
89.5
99.5
130
450
EXA MP L E OF A FREQ UENCY
P O LY G O N
F R E Q U E N C Y P O LY G O N S F O R
G R O U P E D D ATA
A...
...Statistics1
1. One thousand candidates sit an examination. The distribution of marks is shown in the following grouped frequency table.
Marks1–1011–2021–3031–4041–5051–6061–7071–8081–9091–100
Number of candidates155010017026022090453020
(a) Copy and complete the following table, which presents the above data as a cumulative frequencydistribution.
(3)
Mark£10£20£30£40£50£60£70£80£90£100
Number of candidates1565905
(b) Draw a cumulative frequency graph of the distribution, using a scale of 1 cm for 100 candidates on the vertical axis and 1 cm for 10 marks on the horizontal axis.
(5)
(c) Use your graph to answer parts (i)–(iii) below,
(i) Find an estimate for the median score.
(2)
(ii) Candidates who scored less than 35 were required to retake the examination.
How many candidates had to retake?
(3)
(iii) The highestscoring 15% of candidates were awarded a distinction.
Find the mark above which a distinction was awarded.
(3)
(Total 16 marks)
2. At a conference of 100 mathematicians there are 72 men and 28 women. The men have a mean height of 1.79 m and the women have a mean height of 1.62 m. Find the mean height of the 100 mathematicians.
(Total 4 marks)
3. The mean of the population x1, x2, ........ , x25 is m. Given that = 300 and
= 625, find
(a) the value of m;
(b) the standard deviation of the population....
...illustrate trends, etc.
TO ADVOCATE AN ISSUE
TO SHOW THE STATUS OF AN INDICATOR
TO COMPARE INDICATORS
TO DEMONSTRATE CORRELATIONS
TO ILLUSTRATE TRENDS
INFOGRAPHICS USING EXCEL
Frequency Tables and Histograms Charts : create and format charts Conditional Formatting Sparklines Excel Graphics
FREQUENCYDISTRIBUTION
Shows how many observations fall in various categories(bins) Can be represented in a Frequency Table To obtain a Frequency Table for any given data, we must first choose appropriate number of bins Each bin defines a “slot” where some values may fall in There is no set rule for choosing no of bins (good practice is 8 to 15) Need enough categories to get a meaningful distribution, but too many categories will result in few observations per category
A FREQUENCY TABLE OF MARKS OBTAINED
Mark Range (Bins) 12 34 56 78 910
Frequency
2 15 25 18 5
HISTOGRAM
A histogram is the graphical analog of a frequency table Histograms show the frequency with which various category/bin values appears in the data set (e.g., how many students received marks between 2 and 3) The Xaxis of a histogram shows the possible categories and the Yaxis show the frequency
CREATING A HISTOGRAM IN EXCEL
Identify the bins, and define bin range Create Frequency Table and...
...FREQUENCYDISTRIBUTION
WHAT IT IS Frequencydistributions summarize and compress data by grouping it into classes and recording how many data points fall into each class. That is, they show how many observations on a given variable have a particular attribute. For example, a survey is taken of 50 people's favorite color. The frequencydistribution might indicate 15 people selected green, 12 blue, 6 red, 7 yellow, and 10 purple. Converting these raw numbers into percentages would then provide an even more useful description of the data. The frequencydistribution is the foundation of descriptive statistics. It is a prerequisite for both the various graphs used to display data and the basic statistics used to describe a data set  mean, median, mode, variance, standard deviation, and so forth. Note that frequencydistributions are generally used to describe both nominal and interval data, though they can describe ordinal data.
WHEN TO USE IT A frequencydistribution should be constructed for virtually all data sets. They
are especially useful whenever a broad, easily understood description of data
concentration and spread is needed. Most data provided by third parties are
grouped into a frequencydistribution.
Preparation The steps in preparing frequency...
...travelers are asked which midwestern city they prefer: Indianapolis, Saint Louis, Chicago, or Milwaukee. 120 liked Indianapolis best, 430 liked Saint Louis, 1360 liked Chicago, and the remainder preferred Milwaukee. Develop a frequency table and a relative frequency table to summarize this information. (Round relative frequency to 3 decimal places.) 
City  Frequency  Relative Frequency 
Indianapolis  120  0.060 
St. Louis  430  0.215 
Chicago  1,360  0.680 
Milwaukee  90  0.045 

(a)  What is this chart called? 
 
 Histogram 
(b)  What is the total number of frequencies? 
 
 100 
(c)  What is the class interval? 
 
 5 
(d)  What is the class frequency for the 25 to 30 class? 
 
 10 
(e)  What is the relative frequency of the 25 up to 30 class? (Round your answer to 2 decimal places.) 
 
 .10 
(f)  What is the midpoint of the 15 up to 20 class? (Round your answer to 1 decimal place.) 
 
 17.5 
(g)  On how many days were there 10 or more packages shipped? 
 
 5 
award:
12.50 out of
16.66 points
The following frequencydistribution reports the number of frequent flier miles, reported in...