Explore BrainMass

# Dispersion and Spread of Data

### Mean and the standard deviation for frequency distribution

Determine the mean and the standard deviation of the following frequency distribution. Class Frequency 0 up to 5 2 5 up to 10 7 10 up to 15 12 15 up to 20 6 20 up to 25 3

### Range, Arithmetic Mean Income, Population Variance, Standard Deviation

The annual incomes of the five vice presidents of TMV Industries are: \$125,000; \$128,000; \$122,000; \$133,000; and \$140,000. Consider this a population. 1. What is the range? 2. What is the arithmetic mean income? 3. What is the population variance? The standard deviation? 4. The annual incomes of officers of another firm

### Probability calculations based on normal probability

1. Suppose that the random variable x is normally distributed with mean = 1,000 and standard deviation = 100. Sketch and find each of the following probabilities: a. P(1,000<_x<_1,200) e. P(x<_700) b. P(x>1,257) f. P(812<_x<_913) c. P(x<1,035) g. P(x>891) d. P(85

### Stem and leaf, means, standard deviations, t-testing

In order to study the return on assets in the bio-techinlohy industry, a sample of cmpanies was selected randomly. Their rate of returns (X in percent) are shown in the attached document. A) Prepare stem and leaf display B) Calculate the mean rate of return and standard deviation of the rates of return C) If the reat of re

### Mean and Standard Deviations

Advertising expenses are significant component of the cost of goods sold. Listed below is a frequency distribution showing the advertising expenditures for 60 manufacturing companies located in the Southwest. Estimate the mean and the standard deviation of advertising expense. See attached file for chart.

### Calculating Sample Size with Confidence Level and Standard Deviation

We want to estimate the population mean within 5, with a 99 percent level of confidence. The population standard deviation is estimated to be 15. How large a sample is required?

### Finding a variance, given a dispersion matrix

Q: Let A be a 3 x 1 vector of random variables such that: D[A] = mat[5 2 3; 2 3 0; 3 0 2], where D[A] is the dispersion matrix of A. Find the variance of Y = A1 - 2A2 + A3. See attachment for a cleaner version of the question.

### Quartiles, deciles, and various percentiles.

The Thomas Supply Company, Inc. is a distributor of small electrical motors. As with any business, the length of time customers take to pay their invoices is important. Listed below, arranged from smallest to largest, is the time, in days, for a sample of The Thomas Supply Company, Inc. invoices. a. Determine the first and t

### Normal Probability..

Ayrshire cows average 47 pounds of milk a day with a standard deviation of 6 pounds. For Jersey cows the mean daily production is 43 pounds, with a standard deviation of 5 pounds. Assume that normal models describe milk production for these breeds. One farmer has 20 jerseys, while a neighboring farmer has 10 Ayrshires. What'

### Question on Basic Statistics

I need to research the definition of what is called the distribution of a data population. Also, I need to find the statistic that measures the width of dispersion ("looseness" or "tightness") of the population data about its mean.

### Given data, how to find the 3rd quartile

The following data represents the processing times required to pack 20 randomly selected computer hardware orders for mailing: 5.62 16.25 11.46 8.45 5.41 11.62 7.5 4.42 7.58 7.54 5.29 10.92 21.62 8.58 11.42 7.29 7.96 10.5 9.29 8.92 What is the third quartile? A. 10.92 B. 11.05 C. 11.42 D. 11

### Role of population standard deviation in hypothesis testing

1.Discuss and compare testing a claim about a mean when: - the population standard deviation is known - the population standard deviation is unknown

### Computing z values

A recent article in the Cincinnati Enquirer reported that the mean labor cost to repair a heat pump is \$90 with a standard deviation of \$22. Monte's Plumbing and Heating Service completed repairs on two heat pumps this morning. The labor cost for the first was \$75 and it was \$100 for the second. Compute z values for each and

### Median, Quartile, Decile

Kevin Horn is the national sales manager for National Textbooks, Inc. He has a sales staff of 40 who visit college professors all over the United States. Each Saturday morning he requires his sales staff to send him a report. This report includes, among other things, the number of professors visited during the previous week. Lis

### Standard Deviation: Population Means

The mean annual family income for 75 people making inquiries at the first development is \$150,000.00, with a standard deviation of \$40,000.00. A corresponding sample of 120 people at the second development had a mean of \$180,000.00 with a standard deviation of \$30,000.00. At the .05 significance level, can Jones conclude that

### Control Plan Problem

Problem #1 According to the control plan, 8 bolts will be measured every half hour and the machine will will be stopped if it is out of adjustment. Ninety-five percent of the bolts should be within 4+ or - .0004 inches. The last act of 8 showed the following measurements: 4.001 3.998 4.009 3.997 3.990 4.002 3.998

### Mean & Standard Deviation of Time Required for Chemical Reaction

Laboratory data show that the time required to complete two chemical reactions in a production process varies. The first reaction has a mean time of 40 minutes and a standard deviation of 2 minutes; the second has a mean time of 25 minutes and a standard deviation of 1 minute. The two reactions are run in sequence during product

### Standard Deviation Statistics

A young advertising executive for Orlando Dining was not satisfied when her junior analyst gave her the point estimate that the average number of magazines sold per month was 11,500. She wanted to know more than just a point estimate. What do you think her next statistical request was of the junior analyst?

### Propagation of error: The pH of a solution

The pH of a solution is found to be 7.45 ±0.04. What is the error in the concentration of H+ ion?

### Statistics with Z scores and Bayesian Statistics

1. What is the term Bayesian statistics used to indicate? 2. What are the states of nature? 3. What is a variable? 4. What is a z score? 5. How does a z score differs from a t score? 6. What does the symbol sX represent? 7. What is the symbol for standard deviation? 8. What is one formula that we can use to calcula

### "Best Small Companies"

15. A recent article in Business Week listed the "Best Small Companies." We are interested in the current results of the companies, sales and earnings. A random sample of 12 companies was selected and the sales and earnings, in millions of dollars, are reported below.

### Six months after a divorce, the former wife and his band each

Six months after a divorce, the former wife and husband each take a test that measures divorce adjustment. The wife's score is 63 and the husband's score is 59. Overall, the mean score for divorced women on this test is 60(SD=6); the mean score for divorced men is 55(SD=4). Which of the two has adjusted better to the divorce

### Statistics: Arranging Data, Quartiles, Box plot, Mean Problems are attached.

16. Millionaires: The ages of the 36 millionaires sampled are arranged in increasing order in the following table. 31 38 39 39 42 42 45 47 48 48 48 52 52 53 54 55 57 59 60 61 64 64 66 66 67 68 68 69 71 71 74 75 77 79 79 79 a. Determine the quartiles for the data. b. Obtain and interpret the interquartile range.

### Stocks Based on Covariance

You own a stock called Insurate, Inc. Your profit for the stock is a random variable (W) with mean 1,000 and variance 400. You would like to buy more stock and you are trying to decide between Insurate (Y) and Mutual Fund, Inc. (F). Both of these stocks have a mean of 1,000 and a variance of 400. Which stock should you choose gi

### Gamma Distribution

Suppose that when a transistor of a certain type is subjected to an accelerated life test, the lifetime X (in weeks) has a gamma distribution with mean ... (see attachment)

### Percents and probability

The average length of stay in a chronic disease hospital for a certain type of patient is 60 days with a standard deviation of 15. Suppose it is reasonable to assume an approximately normal distribution of lengths of stay. a. What percentage of patients stay less than 50 days? b. Fill in the blanks. The probability is 0.

### Statistics

1. Compute the mean, median, and mode for each of the following distributions. A B C D 3 2 1 2 3 2 3 3 4 2 3 4 6 5 3 4 7 5 5 4 8 7 5 5 10 7 8 7 8 8 8 10 8 8 11 9 11 2. I grew up in a very tiny town in the Midwestern United States. The two had seven streets, and the number of buildings on each street were a

### Data Error

In the process of acquiring data for research, we sometimes find ourselves facing possibility that field workers may have intentionally introduced error into the data. (A) Why and how might they have done this? (B) What can we do to prevent such errors?

### Standard Deviant - How Large of a Sample

A researcher is interested in the average amount of sugar that kindergarten kids eat per day within 4 grams. In a preliminary sample of 36 kids, the amount consumed ranged from 105 grams to 305 grams. The researcher wants to be 97% confident that the margin of error will not be exceeded. How large of a sample must she do if she

### Range, Std. dev., and Variance

The number of cars that travel through an intersection between noon and 1pm is measured for 30 consecutive days. The results of the 30 observations are: 61,62,63,63,64,64,66,66,67,68,68,68,68,69,69,69,69,70,70,70,70,71,71,72,73,74,74,75,76,and 79 Find: a.) Range b.) Standard Deviation c.) The population standar