Explore BrainMass

# Distribution of Data

The distribution of data refers to characteristics used in statistics, such as kurtosis and skewness, which provide detail on the shape of a probability distribution. In statistics and probability, the concept of data being normally distributed is critical to understand and is inextricably linked to the central limit theorem. Essentially, the central limit theorem states that whenever the sample size of a random population is large and the standard deviation and variance of that population is defined, a distribution function can be attached to that population which has a tendency for normality (1). Under the normal distribution, the data points of a random population will always converge at an average value, thus these values will fall within the normal distribution range. Furthermore, as long as the population which is being considered is normal, a sample distribution of the mean will show normality even if the sample size evaluated is small (1).

Considering that in statistics the distribution of data should follow a pattern of normality, being able to test whether a population or a set of data is in fact normally distributed is critical. This is where these characteristics which measure the distribution of data fit in. For example, testing the skewness of a data set is a common method for testing normality. Histograms are often constructed to test whether or not a data set is skewed. If the bars of a histogram display the bell-shaped curve, this illustrates that the data is normally distributed.

Analyzing the distribution of data is integral to the study of statistics since much of this field of study is based on this concept of normality. Therefore, understanding the characteristics which can test for normality is important to being able to interpret data properly and make accurate conclusions.

Reference:

1. Probability and Statistics for Engineers, Eighth Edition – Prentice Hall 2011

## BrainMass Categories within Distribution of Data

### Kurtosis

Solutions: 1

Kurtosis is a characteristic used in probability to measure the peakedness of a probability distribution.

### Skewness

Solutions: 10

Is a characteristic associated with probability distributions, which measures a distribution’s degree of asymmetry.

### Variance

Solutions: 244

In statistics, variance is measured to calculate the total spread of the values in a data set.

### Biostatistics Homework

Biostat 310 Homework 1 TOTAL: 15 POINTS There are a total of 13 graded points (questions indicated by "*") and then an additional 2 points in total for the additional questions without an asterisk, graded according to: 0= no additional problems attempted; 1 = some additional problems incomplete or showing little effort; 2 =

### One-way ANOVA with Post-Hoc Tests Using SPSS

The data file contains the individual data from 102 different participants. An equal number of participants (n=34) were tested in each of the three conditions (Method of Limits, Method of Constant Stimuli, and Method of Adjustment). The task is to analyze the data to determine if there are any significant differences in eithe

### Statistics: histograms and bell shape curves

Need instruction on how to draw the histogram for the following data to determine what the bell curve distribution looks like. In excel if possible. Please see attached file. I can't graph axis's to reflect the story that I am trying to determine which is to find out which distribution is more bell shaped. Thank you,

### The Distribution of Scores

1. The distribution of SAT scores is normal with µ=500 and σ=100. a. What SAT score, x-value separates the top 15% of the distribution from the rest? b. What SAT score. X-value separates the top 20% of the distribution from the rest? c. What SAT score. X-value separates the top 25% of the distribution from the rest? 2. O

### Normal Distribution, Standard Deviation, and Z-Score

1. What is sampling with replacement and why is it used? 2. What proportion of a normal distribution is located between each of the following z-score boundaries? a. z=-0.50 and z=+0.50 b. z=-0.90 and z=+0.90 c. z=-1.50 and z=+1.50 3. Find the z-score location of a vertical line that separates a normal distribution as de

### PSY2007 Sample Question W2A2 can you help with this problem

Imagine that you are collecting data to determine what factors influence an individual's general satisfaction with life. You decide to examine several possible variables and measure the three aspects of life satisfaction. Collect the following data from nine individuals from diverse backgrounds (i.e., they should not all be fami

### Probability of Computers Crashing

Consider a system that has 4 computers. The system is down if at least one computer crashes. The system works if all 4 computers are working. During each day, the probability that a single computer crashes is 5%, independent of other computers and other days. (a) (4 points) Let us first focus on one day. What is the probabili

### Point Estimate and Confidence Intervals for Standard Deviation

A random sample of n = 9 wheels of cheese yielded the following weights in pounds, assumed to be N(μ, σ^2): 21.50 18.95 19.40 19.15 22.35 22.90 22.20 23.10 (a) Give a point estimate for σ. (b) Find a 95% confidence interval for σ and then find a 90% confidence interval for σ.

### Standard Deviation of Sampling Distribution of the Sample Mean

Suppose that we will take a random sample of size n from population having mean µ and standard deviation σ. For each of the following situations, find the mean, variance, and standard deviation of the sampling distribution of the sample mean: (a) µ = 12 , σ = 2.2 , n = 25 (Round your answers of "σ " to 4 decimal place

### Stocks and Populations

The following data represent the responses (Y for yes and N for No) from a sample of 40 college students to the question "do you currently own shares in any stocks?" NNYNNYNYNYNNYNYYNNNY NYNNNNYNNYYNNNYNNYNN A. Determine the sample proportion, p, of college students who own shares of stock. B. if the population proporti

### Sampling Plan - Choosing a Method of Sampling

You are designing a direct marketing campaign for an online clothing retailer. As part of your design, you quantify the expected response rates by ethnic group. Your definition of the term "ethnicity" follows that of the U.S. Census Bureau (e.g., Hispanic, Asian, African American, etc.). You want to test your campaign using 1,00

### Uniform dist., simulations

Create U and V both Uniform on [0,1]. Use excel to generate this data. (10000 data points in each set (U will have 10000 data points and V will have 10000 data points.) Create another set: X=U*V. Using the parameters for U and V compute the theoretical values for E(X), E(U), E(V) and Var(X), Var(U), Var(V). Then using

### Calculating the mean, variance and standard deviation

Find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p. n = 123, p = 0.26 The mean is ______ The variance is ______ The standard deviation is ______

### Miles per Gallon Calculation

Engineers for a major automobile manufacturer are studying the impact of horsepower and weight on the miles per gallon (MPG) obtained by various automobiles. A sample of 30 automobiles is used, and the following regression model is found: Y = 60 â?" 0.15X1 â?" 0.006X2 Where, Y = MPG X1 = horsepower X2 = weight For this

### Name an example of a causal model.

Which of the following is an example of a causal model? Please give brief reasoning supporting your answer. a. An exponential smoothing model b. A weighted moving average model c. A regression model d. The MSE (Mean Square Error)

### Levels of Measurement: Unemployed citizens in the U.S.

Each week, the U.S. federal government receives data from 20 state unemployment offices, detailing how many people are receiving unemployment benefits, how many people have run out of unemployment insurance, and how many people are no longer actively seeking employment. After making adjustments for the calendar date, the govern

### Expected value, variance & standard deviation

4.11 An investment syndicate is trying to decide which two \$200,000 apartment houses to buy. An advisor estimates the following probabilities for a five-year net returns ( in thousands of dollars): Return: -50 0 50 100 150 200 250 Probability for house 1: .02 .03 .20 .50 .20 .03 .02 Probability for house 2: .15 .10 .10

### 10 Statistics problems: Pooled variance, interval data, t-test, unpaired data, z-test

1. What is pooled variance and why is it important? 2. Explain what interval data is and give an example: 3. Write the formula for a problem that has 2 sample populations greater than 30 and the standard deviations are known and equal: 4. Write the formula for pooled variance. 5. Please analyze the following data usi

### Assume that sample data represents a population distribution

Why do you want to assume that your sample data represents a population distribution?

### Pooled Variance, Interval Data and Hypothesis Testing

1. What is pooled variance and why is it important? 2. Explain what interval data is and give an example: 3. Write the formula for a problem that has 2 sample populations greater than 30 and the standard deviations are known and equal: 4. Write the formula for pooled variance. 5. Please analyze the following data usi

### Range, Variance & Standard Deviation

Researchers conducted experiments with trees. Listed below are wights (kg) of trees given no fertilizer and trees treated with fertilizer and irrigation, Find the range, variance and standard deviation for each of the two samples, then compare the two sets of results. Does there appear to be a difference between the two stand

### Inventory & Forecasting Questions

Explain how to use seasonal index values to create a forecast. In the solution of the assignment problem, the opportunity lost is the difference between the a. smallest value in the column and the value in the cell. b. largest value in the row and the value in the cell. c. smallest value in the row and the value in the

### What would be the mean, variance, standard deviation and shape of the distribution of sample means?

If many samples of size 15 (that is, each sample consists of 15 items) were taken from a large normal population with a mean of 18 and variance of 5, what would be the mean, variance, standard deviation and shape of the distribution of sample means? Give reasons for your answers. Note: Variance is the square of the standard d

### Expected Value, variance and standard deviation

The number of customers waiting at any given time is described in the table below. # of Customers X 1 2 3 4 5 Probability P(X) 0.15 0.32 0.28 0.15 0.10 Compute the expectation E(X), the variance, and the standard deviation. Please show me calculations on how it's done without using an advanc

### Finding Mid Range, Standard Deviation and Variance

Monthly sales figures for a store are as follows: Jan \$62k Feb \$71k Mar \$68k Apr \$47k May \$71k Jun \$69k Jul \$80k Aug \$75k Sept \$87k Oct \$77k Nov \$63k Dec \$70k Find the: a.Mid-range b.Standard Variance c.Standard Deviation

### Randomness in a Data File

What is randomness? Assume you have an Excel worksheet of the dimension, A1:E101. The first row contains data labels. How would you randomize the data file and to select a simple random sample of 10 items from the dataset?What are N, Ni and n?

### Variance and Standard Deviation..

1.A random sample of 5 dates is selected and a standard deviation is calculated for these 5 dates. The dates and the respective temperatures are: Date Temperature August 1 94 August 3 99 August 8 78 August 11 88 August 14 88 What is the variance

### Expected value, variance, standard deviation

Shown is a probability distribution for the random variable x f(x) 3 0.25 6 0.50 9 0.25 Total 1.00 a. Compute E(x), the expected value of x. b. Compute o^2, the variance of X c. Compute o, the standard deviation of X.

### Mean, Range, Variance, Standard deviation

The weights (in pounds) of a sample of five boxes being sent by UPS are: 12, 6, 7, 3, and 10. a. Compute the mean for this sample. b. Compute the range for this sample. c. Compute the variance for this sample. d. Compute the standard deviation for this sample. Show your work!

### Variance and Standard Deviation: Measure of Variation

A dietitian obtains the amounts of sugar (in centigrams) from 100 centigrams (or 1 gram) in each of 10 different cereals, including Cheerios, Corn Flakes, Fruit Loops, and 7 others. Those values are listed below. Is the standard deviation of those values likely to be a good estimate of the standard deviation of the amounts of su