1. A manufacturer of hand shovels is deciding what length handles to use. Studies of user preference reveal that the average, the median, mean and mode of preferred length are all different. What are the implications of using each of these values? Which value would you decide?
2. A given machine is assumed to depreciate 40 percent in value in the first year, 25 percent in value in the 2nd year and 10 percent in value in the next three years; each percentage is being calculated on the diminishing value. What is the average percentage depreciation, reckoned on the diminishing value for the five years?
3. The mean age of a group of 100 persons was found to be 32.02.Later, it was discovered that age 57 was misread as 27. Find the corrected arithmetic mean.
4. Out of the total population of certain town in South Africa 60% belonged to the Black Race and the rest belonged to the white race. It was estimated that their mean incomes were 2000 and 5000 pounds respectively. Find the average income of the entire town?
5. The following data represents travel expenses (other than transport) for trips made during November by a salesman of a firm.
An auditor criticized these expenses as excessive asserting that the average expense per day is Rs10/ (Rs 70 divided by 7). The salesman replhed that the average is only Rs 4: 20 (Rs105 divided by 25) and that in any evejt the median is the appropriate measure and is only Rs3. The auditor rejoined...
...
Subject: Math – Measures of CentralTendency
Grade: 6th
GLE Standard: Mathematics  Data and Probability. 2. Select and use appropriate statistical methods to analyze data. A. Describe and analyze data  find the range and measures of center, including median, mode, and mean.
Materials:
 Bag of mixed candy, or something comparable the students can sort and count
 Whiteboard/blackboard
 Computer and display ability
 Legal sized paper or construction paper
Objectives/Learning Targets: By analyzing a set of data, students will be able to calculate mean, median, mode, and range.
Introduction:
 After greeting the class show a short video, on mean, median, mode, and range, called “Measures of CentralTendency Rap” http://www.youtube.com/watch?v=1jVZi0cNHls
 Give the students a Handout highlighting the key concepts of mean, median, mode, and range, as well as some example problems and the steps to work them
 Next, show the class a large bag of assorted candy, for example a 105 count bag of assorted Easter candy, and ask the class to guess the amount of each candy type
 Finally, group students and distribute the candy (so the students can be ready to sort and count the candy)
Lesson Procedure:
Modeling/Teaching: With the help of the students, separate the various candy types and count how many of each type...
...Introduction to Statistics (Measures of CentralTendency)
CentralTendency: In a representative sample, the value of a series of data have a tendency to cluster around a certain point usually at the center of the series is usually called centraltendency and its numerical measures are called the measures of centraltendency or measures of location.
Different Measures of CentralTendency: The following are the important measures of centraltendency which are generally used in business:
Arithmetic mean
Geometric mean
Harmonic Mean
Median
Mode
Arithmetic mean: Arithmetic mean is defined as the sum of all observations divided by the total number of observations.
Calculation of Arithmetic MeanUngrouped Data: For ungrouped data, arithmetic mean may be computed by applying any of the following methods:
Direct method
Shortcut method
Direct method: The arithmetic mean, often simply referred to as mean, is the total of the values of a set of observations divided by their total number of observations. Thus, if represent the values of items or observations, the arithmetic mean denoted by is defined as:
If the subscripts are dropped, the formula sample mean is: = and the population mean is:
Shortcut method: According to shortcut method arithmetic mean can be...
...Week Five Discussion

This Discussion will give you the opportunity to calculate or identify the three measures of centraltendency. You will be asked to select an appropriate real life situation in which one measure would be more appropriate than the other two measures of center.
1. Select a topic of interest to you and record the topic in your posting, for example: “What is the average number of hours people watch TV every week?” Make sure the question you ask will be answered with a number, rather than answers with words.
What is the average number of hours people read every week?
2. Write a hypothesis of what you expect your research to reveal. Example: Adults 21 years and over watch an average of 2.5 hours of TV per day.
On average, people read about 15 hours per week.
3. Sample at least fifteen people and record their data in a simple table or chart; study the examples from Section 123.
PERSON  AGE  GENDER  HOURS READ PER WEEK 
1  17  F  8 
2  16  F  10 
3  14  F  5 
4  37  M  4 
5  38  F  20 
6  33  F  5 
7  22  F  30 
8  52  F  30 
9  40  F  18 
10  21  M  3 
11  16  F  14 
12  13  M  5 
13  36  F  25 
14  27  F  20 
15  43  F  25 
4. You can gather your data at work, on the phone, or via some other method. This is your “Sampling Design.” Which of the four sampling techniques best describes your design?
Out of...
...REPORT
ON
“Use of CentralTendency and Dispersion in Business Decision”
Course Title: Business Statistics
Course Code: STS201
Submitted To: Mr. Raihanul Hasan
Senior Lecturer
Submitted By:
Date of submission: 261212
BBA PROGRAM
STATE UNIVERSITY OF BANGLADESH
We can use single numbers called “Summary Statistics’ to describe characteristics of a data set. Two of these characteristics are particularly important to decision makers:
1. Centraltendency
2. Dispersion
Measures of centraltendency and dispersion provide a convenient way to describe and compare sets of data.
CentralTendency:
Centraltendency is the middle point of a distribution. Measures of centraltendency are also known as Measures of location. Measures of centraltendency yield information about the center, or middle part, of a group of a numbers. It does not focus on the span of data set or how far values are from the middle numbers.
Dispersion:
Dispersion is the spread of the data in a distribution, that is, the extent to which the observations are scattered.
Objectives:
* To use summary statistics to describe collection of data.
* To use the mean, median and...
...1 Measures of CentralTendency
“Measures of centraltendency (averages) are statistical constants which enable us to figure out in a single effort the significance of the whole.” (Prof Bowley)
The main objectives of measure of centraltendency are
To reduce data in a single value.
To make easy comparisons between data.
There are different types of averages; each has its own business applications.
1. Arithmetic Mean
2. Median
3. Mode
4. Geometric Mean
5. Harmonic Mean
1.1 Arithmetic Mean
1.1.1 Definition
Most important measure of location is the mean or average value, for a variable. The mean provides a measure of central location for the data. If the data are for a sample, the mean is denoted by; if the data are for a population, the mean is denoted by the Greek letter μ. (David R. Anderson et al)
1.1.2 Business Applications of Mean
Arithmetic mean is considered a deal average. It is frequently used in all the aspects of business i.e. number of items produced per day on a large assembly line, number of orders received per month for a firm. further In economic analysis arithmetic mean is used extensively to calculate average production, average wage, average cost, per capital income exports, imports, consumption, prices, etc. (www.publishyourarticles.net)
1.1.2.1 Example
Say we want to find the average annual salary of all secretaries. We believe we can...
...CentralTendency and Measures of Variation
Task 1:
1.1 a.) Define Population: Population is a complete group or collection of items or people selected to be used for a statistical study
b.) Define Sample: Sample is a partial selection or part of the population for which the study uses for information gathering.
1.7 The Neilson study is an inferential study; the results contained on the study are not focused and generalized. The population is not defined and therefore inferences are needed to state the results of the data and may not follow the trends of the population that the data being stated about here.
1.14 a.) For the offshore drilling poll, the US Adults are the population used.
b.) The data used here is descriptive of the data gathered in the poll
1.17 The Salk vaccine study was conducted s a designed experiment. This is due to the selected study population being inoculated with or without (placebo) the vaccine to study the results of the two group’s reactions and results
Task 2:
3.8 The family net worth in the Survey of Consumer Finances, the mean net worth of families in the United States was $448.2 thousand and the median net worth was $93.1 thousand. Which measure of center do you think is more appropriate?
A lot depends on what you are looking for here; the mean net worth is the true average worth across the sample. However, the median net takes the extremes out of the worth, meaning the very rich and the...
...Measures of CentralTendency
1. What Do You Mean by Mean?
a) The mean of the salaries is calculated by adding up each individual salary and dividing it by the seven employees. The mean of the seven salaries is $43,814.29. The mean compares to the individual salaries because it shows the average of all the salaries together. The employees would use the average to negotiate with Dick for a higher salary, because by looking at the average you can see that Dick’s salary is an outlier compared to the mean.
b) The median of these seven salaries is $23,500. I got the median by first putting the numbers in order. Since it is an odd amount of numbers, I just find the center of the data after they were in order. This value does not really compare to all of the individual salaries; it has no relation other then it is just in the center. Dick’s salary does not compare to the median because it is the outlier, but mostly everyone else’s does because it is around the same amount.
c) The mean gives a fairer sense of the “average” salary because since Dick’s salary is an outlier so the median is automatically not appropriate to describe all the salaries. The mean sort of equally describes all the salaries because it is in the middle of each. The median describes the majority of the salaries, but not Dick’s because it is an outlier.
2. Better than Average
Each measure of centraltendency has strengths and weaknesses. Not...
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