Sampling and Measures of Central Tendency and Dispersion

Introduction: Overall Job Satisfaction (OJS) was the variable selected for this exercise because it lends itself to measures of central tendency and dispersion. The data are quantitative and continuous in nature.

Data Selected: The instructions for the exercise suggested a sample of approximately 30 individuals from one of eight variables. There were 288 measures of OJS. Every ninth individual was selected resulting in thirty-two (32) unique scores. The data was sorted by gender (17 males, 15 females) as shown in the following table:

Discussion: Microsoft Excel software was used for all calculations.

The arithmetic mean (average) was calculated to be 4.56. It is understood that this measure of central tendency is affected by extreme scores.

The median (middle value) for this even numbered sample of 32 is 4.6. This value suggests that the mean is being affected by scores indicating some degree of dissatisfaction.

...Assignment on CentralTendency and Dispersion
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.
Trip Days Expense Expense per day
1 .5 13.50 27.00
2 2 12.00 6.00
3 3.5 17.50 5.00
4...

...
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...

...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,...

...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...

...Measures of CentralTendency
Objectives of the chapter
• To use summary statistics to describe collections of
data
• The main goal is to come up with the one single
number that best describes a distribution of scores.
• Lets us know if the distribution of scores tends to be
composed of high scores or low scores.
• To use the mean, median and mode to describe how
data bunch up.
The sales of 100 fast food shop is
given below:
Sales
No. of
(in 000s) Shops
700-799
4
800-899
7
900-999
8
1000-1099 10
1100-1199 12
1200-1299 17
Sales
(in 000s)
1300-1399
1400-1499
1500-1599
1600-1699
1700-1799
1800-1899
No. of
shops
13
10
9
7
2
1
Measure of CentralTendency
The following are the important measures of
CentralTendency
a)Mean b) Median and c) Mode
Mean can be classified as three types:
i) Arithmetic mean
ii) Geometric mean
iii) Harmonic mean.
Measure of CentralTendency
An average (mean) is a single value which is
considered as the most representative or
typical value for a given set of data.
Such a value is neither the smallest or the
largest value, but is a number whose value is
somewhere in the middle of the group.
Measure of Centraltendency show the tendency
of some central value around which data tends
to cluster....

...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...

...Module on Measures of
CentralTendencyMeasures of CentralTendency
There are many ways of describing of a
given set of data. A good number of descriptive
measures exist in statistics whose use depends
largely on the nature of data and the intended
purpose of the description. This measure is the
measures of position or centraltendency, it is
use to see how a large set of raw materials can
be summarized so that the meaningful essential
can be extracted from it.
The most commonly measures of centraltendency are the mean, median, and mode.
Properties of the Arithmetic Mean
easy to compute
easy to understand
valuable in statistical tool
strongly influence by extreme values,
this is particularly true when the number
of cases is small
cannot be compute when distribution
contains open-ended intervals
Uses of Mean
for interval and ratio measurement
when greatest sampling stability is
desired
when the distribution is symmetrical
about the center
when we want to know the “center of
gravity” of a sample
The Arithmetic Mean (X)
The most popular and useful measure of centraltendency is the arithmetic
mean, which simply refer to as the mean. Widely referred to in everyday usage as the
average.
The mean of a...

...Measures Of CentralTendency: Mean Medium Mode
Mode instead of mean… Categorical variables, words not numbers
Measures of Dispersion: Standard Deviation, Range, and Variables
Range = Largest number minus smallest number
SD = Average Distance from the Mean (Most frequently used)
Variance:
Fat & Skinny Distributions: Skewness – measure of the lack of symmetry, or the lopsidedness of a distribution.
One “tail” of the distribution is longer than another.
Kurtosis: has to do with how flat or peaked a distribution appears/
Platykurtic: flat
Leptokurtic: peake
Hypotheses
Null Hypothesis: There is NO RELATIONSHIP between our IV and DV
Non-Directional Hypothesis:
Directional Hypothesis: We believe we know the direction
What makes a good hypothesis?
Testable
Can’t be in a question
Tell a relationship between
Stated in a declarative form
Brief and to the point
Reflects theory or past literature
Tells a relationship between variables
The Normal Curve
The Bell Shaped Curve
Mean=Median=Mode
Symmetrical
Asymmetric Curve
Statistical Inference
The Central Limits Theorem: When samples are large (above 30) the sampling distribution will take the shape of a normal distribution regardless of the shape of the population
Ultimate Goal
Accepting or Rejecting the NULL hypothesis
Accept or Reject?...

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