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For the following sample of scores, compute the (a) mean, (b) variance, and (c) standard deviation:12, 14, 15, 18, 22, 25, 26, 30.

1.For the following sample of scores, compute the (a) mean, (b) variance, and (c) standard deviation: 12, 14, 15, 18, 22, 25, 26, 30.

2.For a population with a mean of µ = 100 and a standard deviation of σ = 12,

  1. Find the z-score for each for the following x-values.

x = 106

x = 91

x = 115

x = 130

x = 61

3.Find the score (x-value) that corresponds to each of the following z-scores.

z = -1.00

z = 0.75

z = -.50

z = 1.50

z = 2.00

z = -1.25

4.A population distribution with a mean of µ = 56 and a standard deviation of σ = 20 is transformed into a standardized distribution with µ = 50 and σ = 20. Find the new, standardized scores for each of the following values from the original population.

x = 46

x = 76

x = 40

x = 80

5.Draw a vertical line through a normal distribution for each of the following z-score locations. Determine whether the body is on the right or left side of the line and find the proportion in the body.

z = 2.20

z = 1.60

z = -1.50

z = -0.70

SPSS Portion: Please append all output to the homework assignment when you turn it in!

6.A local government operates a small park near its city hall. The department uses the attendance to measure its workload in determining the budget for the park. The city manager has long believed that the park has too few visitors and that the department should reach out to more customers or its budget will need to be reduced. You are an analyst for the city. The city manager has asked you to do an analysis for the park to determine whether the budget request for the park is justified in the city's budget proposal. You randomly selected 25 days in the past year and calculated the park attendance data: 5, 3, 10, 1, 2, 3, 4, 3, 5, 100, 4, 3, 2, 4, 25, 150, 3, 3, 5, 4, 8, 7, 10, 15, and 30.

  1. Use computer software (SPSS) to calculate the mean, the median, and the mode for the data. Explain the meaning of these statistics. Do you recommend the use of the mean in your presentation? Why or why not? Do you recommend the use of the median or the mode? Why or why not?

7.Using the Community Indicators dataset, calculate the mean burglary rate per capita. To get this done, you first need to make new variable, which is the burglary rate per capita for each city in the dataset. Let's call this variable "burglaryrate" and define it as burglary/pop, whereby "burglary" and "pop" correspond to the variable names in the Community Indicators dataset. Use your statistical software program to calculate the mean and median burglary rates per capita. 

  1. Which three cities have the highest burglary rates per capita? Are these the same cities as those with the largest number of burglaries?

8.Standard deviation is a useful concept in performance management. It can be useful in performance comparison, performance monitoring, and performance evaluation. Let's say that a director in a local fire department wants to know any variation between the performance of this year and that of last year. He draws a sample of 10 response times from this year (in minutes): 3.0, 12.0, 7.0, 4.0, 4.0, 6.0, 3.0, 9.0, 11.0, 15.0, comparing them with a sample of 10 response times from last year (in minutes): 8.0, 7.0, 8.0, 6.0, 6.0, 9.0, 7.0, 9.0, 8.0, 6.0.

  1. Does he see a performance variation by the mean? 
  2. Does he see a performance variation by the standard deviation? If he does, is it a performance improvement or a performance deterioration from the last year? Why?
  3. Now, imagine that you are a citizen receiving fire protection services from this local fire department. How do you evaluate the response times of this fire department, by the mean, by the standard deviation, or by both?
  4. If the average response time improves (shortens) but the standard deviation of the response times deteriorates (increases), what is your conclusion of the performance as a service recipient? In other words, do you want a quicker average response at the expense of a more unpredictable response? What is your recommendation to the director on which statistical measures he should use and how he should use them?
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