# Analyzing Data

The data set for our course is a sample of a survey conducted on the population of the American Inmate Union (AIU). It is available via the attachment: DataSet with DataSet Key, which contains the following nine sections of data that will be used throughout our course:

Gender

Age

Type of Offense

Prison Facility

Length of Sentence

Criminal Justice System

Legal Services- Satisfaction with the actual performance of attorney

Sentence satisfaction-

Incarceration Services - Health, food, vocational training, etc.

American Inmates Union (AIU) has assembled a team of researchers in the United States and around the world to study inmates' satisfaction with the criminal justice system. Congratulations, you have been selected to participate in this massive global undertaking.

The study will require that you examine data, analyze the results, and share the results with groups of other researchers. Inmates' Satisfaction is important to all criminal justice organizations large and small and understanding inmates' concerns provides criminal justice management with insights into areas that can be modified and used to strengthen the criminal justice system.

Examine two of the nine sections of data - one section of qualitative data (Gender, Position, etc.) and one section of quantitative data (Legal Services Satisfaction, Sentence Satisfaction, etc.), from the provided data set through the link above. Each section should include all data points listed in the column for the variable.

The requirements include identifying the data you selected, discussing why the data was selected and what was learned by examining these sets of data. Your analysis should include using Microsoft Excel to obtain information about the data through the use of three measures of central tendency (mean, median, and mode) and the use of two measures of variability (standard deviation and variance). Some measures are appropriate for qualitative data and some are appropriate for quantitative data. If a measure is not applicable, then explain why.

Provide one chart/graph for each of the results of the two processed sections of data (2 total), such as a pie or bar chart or a histogram. (A table is NOT a chart/graph.) Ensure that you label the chart/graph clearly.

Explain why charts/graphs are important in conveying information in a visual format and why standard deviation and variation are important.

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2.A group of 25 subjects have their diastolic blood pressures measured. The results, in SPSS are:

|-----------|-------|--------|

|N |Valid |25 |

|-------|--------|

| |Missing|0 |

|-----------|-------|--------|

|Median |85.00 |

|-------------------|--------|

|Mode |82.00 |

|-------------------|--------|

|Minimum |55.00 |

|-------------------|--------|

|Maximum |110.00 |

|-----------|-------|--------|

|Percentiles|25 |71.00 |

| |-------|--------|

| |50 |85.00 |

| |-------|--------|

| |75 |98.00 |

|--------|-------|--------|

Don't worry about values exactly at the endpoints of these intervals. Do the calculations roughly.

(1 point each)

a. What percentage of subjects were from 55 to 85?

b. What percentage of subjects were < 85?

c. What percentage of subjects were from 71 to 85?

d. What percentage of subjects were > 71?

e. What percentage of subjects were > 98?

f. Is there one value more common than the rest, and if so, what is it?

3. Assume you have already been give a Z value. This saves you a step. Consider and determine the following probabilities (1 point each).

A. Pr (-1 < Z < 1)

B. Pr (0 < Z < 1)

C. Pr (Z > 1)

D. Pr (-1 < Z < 0)

E. Pr (Z < -1)

F. Pr (Z > -2)

G. Pr (-1 < Z < 2)

4. Suppose the mean systolic blood pressure in a group of individuals is 150 mmHg, with a standard deviation of 15. Assuming SBP follows a normal distribution in this population, compute (1 point each):

A. Pr (135 < value < 165)

B. Pr (value > 165)

C. Pr (value < 135)

D. Pr (138.75 < value < 161.25)

5 Compute the 5th, 50th, and 95th percentiles of SBP from the previous question. (3 points: 1 each).

In questions 6 - 8, use the 1 and 2 SD rules, without the table.

6.In general, what percentage of a Gaussian data set is within 1 SD of the mean? What percentage is within 2 SD's of the mean? (2 points: 1 each)

7.If the mean grade on an exam was 80, SD = 6, where did about 68% of the grades fall? How about 95%? Assume the grades are Gaussian. (2 points).

8.Consider the following data: 1, 1, 2, 2, 4, 5, 6, 9, 40, 200

Use the 68% and 95% rules to test the normality of these data. (2 points).

9.A researcher studying a subtype of lymphocytes obtains a sample mean of 100 per mL, and a standard deviation of 20, with 25 subjects. Within what interval can you be roughly 68% sure the population mean number of these cells per mL lies? How about 95% sure? (2 points)

10.A researcher has a sample of 500 subjects. The mean is 40, median is 20, range 10-100. (2 points each)

a.Could this researcher calculate a useful interval with 95% probability of containing the population mean (using the mean and SEM)? Explain

b.Could the researcher use the mean and SD to usefully estimate where 95% of the individual subject values were? Explain

c)If there were 10 subjects, would your answers to a and b change?

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