Share
Explore BrainMass

Dispersion and Spread of Data

The dispersion and spread of data refers to measures in statistics which are used to define the deviation or scatter of a data set from the central value. Some of these measures, such as standard deviation and the interquartile range, are commonly seen marked on graphs to illustrate the variability which exists in the data set being presented. To describe data fully, knowing the extent of variability which is present is critical, and this cannot be achieved through the use of central tendency measures alone (1). Thus, using measures which evaluate the dispersion and spread of data is a common practice.

Using various measures of dispersion or spread in conjunction with measures of central tendency is very valuable in statistics. Using a measure of spread to assess the variability of a data set can provide insight as to whether a particular measure of central tendency will be useful in evaluating the data (2). Determining whether the variation of a data set is high or low can indicate whether or not the mean would be more appropriate than the median to use in finding the average value of a data set.

Essentially, the overall objective in using measures of dispersion and spread is to summarize the nature of data. Calculating the interquartile range, standard deviation or range, are some of the methods which can be implemented to estimate variability. Furthermore, utilizing different indicators of dispersion and spread can be an efficient method for making comparisons between data sets, and thus, educated conclusions regarding the importance of the results.

References: 

1. http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3198538/ 

2. https://statistics.laerd.com/statistical-guides/measures-of-spread-range-quartiles.php

Categories within Dispersion and Spread of Data

Range

Postings: 16

The range is a statistical measure which aims to calculate the spread between the minimum and maximum value in a data set.

Standard Deviation

Postings: 201

Standard deviation is a measure of absolute variation used to calculate the amount of divergence which exists from an expected value and is denoted by the Greek symbol for sigma.

Coefficient of Variation

Postings: 30

The coefficient of variation is computed by deriving the ratio between the standard deviation and the mean and thus, is known as a measure of relative variation.

Percentile

Postings: 49

Percentiles are often calculated for a set of data in statistics and are representative of different percentage ranges.

Interquartile Range

Postings: 9

In statistics, the interquartile range refers to the overall difference between the higher quartile value of a data set and the accompanying lower quartile value.

Build a frequency table and calculate variance for given data

•With included given data which is number of hours worked per day for ten days. Data: 4,2,4,2,4,0,3,2,1,1 •Create a frequency distribution table for your data. You can use Excel or Word. •Calculate the standard deviation. •Calculate the variance. •Is this a normal distribution? How do you know? •What are the i

Standard Deviation of the Sample Mean

A study of the amount of time it takes a mechanic to rebuild the transmission for a 1992 Chevrolet Cavalier shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 36 mechanics are randomly selected, find the probability that their mean rebuild time is less than 8.9 hours. What is the standard deviation of t

Reorder Point Calculation

The president of the wholesale distributor is concerned about the possibility of stockouts causing a loss of customer confidence and loyalty and is interested in maintaining safety stock in inventory to prevent potential stockouts. Assuming demand is normally distributed with a mean of 15 units and a standard deviation of 3

Elementary Statistics Problem Set

2.82 All measures of variation are nonnegative in value for all sets of data. a. What does it mean for a value to be "nonnegative"? b. Describe the conditions necessary for a measure of variation to have the value zero. c. Describe the conditions necessary for a measure of variation to have a positive value. 2.83 Consider

Collecting Data for a Study

If you were designing a study which group, a population or a sample, would you collect data from and why? Provide an explanation regarding whether or not the standard deviation is a biased or unbiased estimate. When comparing the standard deviation to the variance, which do you prefer to interpret and why do you feel this way?

Probability Distribution & Standard Deviation

The New York City Housing and Vacancy Survey showed a total of 59,324 rent-controlled housing units and 236,263 rent-stabilized units built in 194 or later. For these rental units, the probability distributions for the number of persons living in the unit are given. Number of Persons Rent-Controlled Rent-Stabilized 1

Statistics: Breaking Distances of Cars

Assume that both samples are independent simple random samples from populations having normal distributions. A random sample of 13 four-cylinder cars is obtained, and the braking distances are measured and found to have a mean of 137.5ft and a standard deviation of 5.8ft. A random sample of 12 six-cylinder cars is obtained and

Finding the Percentile

I need help solving this problem: The amount of Jen's monthly phone bill is normally distributed with a mean of $50 and a standard deviation of $10. Find the 25th percentile.

Hurricane Katrina

Hurricane Katrina hit New Orleans on August 29, 2005. The National Weather Service Forecast Office maintains online archives of climate data for all U.S. cities and areas. These archives allow us to find out, for example, how the rainfall in New Orleans that August compared to the other months of 2005. The table below shows the

Estimates percent change in population for each U.S. state over

The following table gives estimates of the percent change in population for each U.S. state over the years 1990 to 2000. (This data set was used in Example 1.8.) State Percent Change State Percent Change Alabama 10.1 Montana 12.9 Alaska 14 Nebraska 8.4 Arizona 40

Construct Frequency Distributions Classes

1. Radiation in Baby Teeth: Listed below are amount of strontium-90 (in millibec-querels) in a simple random sample of baby teeth obtained from Pennsylvania residents born after 1979 (based on data from "An Unexpected Rise in Strontium-90 in U.S Deciduous Teeth in the 1990's ," by Mangano, et.al., Science of the Total Environmen

Returns and Standard Deviations

Consider the following information: Rate of Return if State Occurs State of Economy Probability of State of Economy Stock A Stock B Stock C Boom .20 .37 .41 .42 Good .30 .17 .12 .13 Poor .17 .11 .06 .05 Bust .33 .05 -.05 -.04 Requirement 1: Your portfolio is invested 16 percent each in A and C, and 68 perc

Mean and Standard Deviation of Light Bulb Lifetime

The lifetimes of light bulbs of a particular type are normally distributed with a mean of 370 hours and a standard deviation of 5 hours. What percentage of bulbs has lifetimes that lie within 1 standard deviation of the mean on either side?

Mean and Standard Deviation

Many drugs used to treat cancer are expensive. Business week reported on the cost per treatment of Herceptin, a drug used to treat breast cancer (Business Week, January 30, 2006). Typical treatment costs (in dollars) for Herceptin are provided by a simple random sample of 10 patients. 4376 5578 2717 4920 4495 4798 6446

Empirical rule response - please verify and add additional information.

Hello, This is my assignment for Statistics, I answered the question but I want to make sure is well answered and If I am answering right both "explain the empirical rule" and the "when can it be used?". Please feel free to do any changes. Thank you very much. -Explain the empirical rule. When can it be used? The Empiric

Chebyshevs Theorem and Empirical Rule

Please show all of your work when answering the following: I. Use Chebyshevs theorem to find what percent of the values will fall between 162 and 292 for a data set with a mean of 227 and standard deviation of 13. II. Use the Empirical Rule to find what two values 99.7% of the data will fall between for a data

Descriptive Statistics/Describing Variation

Need help with the following problem: Temperature is critical to ensure a proper cure of paint on transformer drums. After the transformer drums are painted, they are sent through an oven. The mean temperature of the oven is 535 degrees F with a standard deviation of degrees of 27 degrees F. The oven temperature is normally d

POST STATISTICS ANSWERS INTO EXCEL FORMAT

PLEASE HELP ME POST QUESTIONS 2.3 AND 2.4 INTO EXCEL FORMAT WITH CALCULATIONS SHOWING. THE QUESTIONS HAVE BEEN ANSWERED ON TAB 1 WHERE IT SAYS QUESTIONS, BUT, I NEED TO PUT THE ANSWER ON THE CORRECT TAB BUT WITH EXCEL CALCULATIONS SHOWING. IVE ONLY PASTED ANSWERS AND THAT'S INCORRECT.

Computations are displayed.

The number of baby deliveries in a medium sized hospital was sampled over 12 hour periods. Below is the sample: 24 16 7 15 11 14 7 16 22 17 22 16 9 17 14 5 16 11 17 19 21 From this data set, compute the sample mean, median, mode and midrange. Compute the 1st quar

Standard Deviation for weight of steers

Using a normal distribution with a mean of 1118 and a standard deviation of 52 for the weights of steers, what percent of steers weigh over 1250 pounds, under 1100 pounds, between 1000 and 1150 pounds.

Ranking in Statistics

Rank the following data in increasing order and find the positions and values of both the 39th percentile and 73rd percentile. Please show all of your work. 5 5 0 0 9 6 8 9 2 6 3 8

Joe's mean and standard deviation of the average payout from his 14,000 bets

The law of large numbers tells us what happens in the long run. Like many games of chance, the numbers racket has outcomes so variable-one three digit number wins $600 and all others win nothing-that gamblers never reach "the long run". Even after many bets, their average winnings may not be close to the mean. For the numbers

Mean Mileage for a Minivan

THE MEAN MILEAGE FOR A CERTAIN MINIVAN IS 19.5 MPG WITH A STANDARD DEVIATION OF 1.8 MPG. A. ASSUMING WE KNOW NOTHING ABOUT THE SHAPE OF THE DATA SET, AT LEAST WHAT % OF TIME WILL THE RECORDED MILEAGE BE BETWEEN 16.8 AND 22.2 MPG? B. ASSUMING WE CAN VERIFY THAT THE DATA SET IS APPROX NORMALLY DISTRIBUTED, WHAT % OF TIME WIL

Statistics

The problem is to estimate that sales for the coming year for a maker of industrial equipment. The forecast is based on askingcustomers how much they are planning to order next year. To use the research budget efficiently, the customers are stratisifiedby the size of their orders during the past year. The following is some relev

40 Mathematics Problems

1. Turner agrees to buy a boat for $2,800 down and $129 a month for 48 months. What is the total cost of the boat? 2. Rocco scored 81, 89, 68, 92, and 77 on his mathematics quizzes. Round each score to the nearest ten to estimate his total score. 3. a) Name the property of addition that is illustrated. 4 +9