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# Statistics and Data Analysis

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1. Explain the difference between data and information.
2. What is the difference between a population and a sample?
3. List the different types of charts available in Excel, and explain characteristics of data sets that make each chart most appropriate to use.
4. What does skewness measure? Interpret the value of the coefficient of skewness as obtained in Excel.
5. What is a proportion? Provide some practical examples where proportions are used in business.

#### Solution Preview

Dear Student:

Q1. Data and Information

In statistics, data refers to raw data that was collected in order to perform a statistical analysis. Data can be nominal (e.g. colors red, blue, green, orange), ordinal (e.g. ranking of a university in a national survey), interval (e.g. temperature, shoe size), and ratio (e.g. amount of money in your bank account).

Information is something that you find in a book or on the internet. It can be correct or incorrect. You determine the reliability of information by looking support in other sources, but you cannot statistically check if it is correct or not.

Q2. Population and sample

Population is a collection of all possible individuals, objects, or measurements of interest. (Lind et al., 2002, p. 7). It can be the population of the United States, all students in your school, or all customers of Macy's.

Sample is a portion, or part, of the population of interest. (Lind et al., 2002, p. 7). You cannot investigate all people in the United States and ...

#### Solution Summary

This solution offers definitions of several statistical concepts: data vs. information, population vs. sample, skewness, and proportion. Examples of each are also given. Also, an introductory explanation of the charts available in Excel is included. This solution does not include calculations.

\$2.19

## BIOSTATISTICS

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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