Chapter 1 A First Look at Statistics and Data Collection

2 Statistics A science comprising of rules and procedures that are used for collection, summarization, presentation, analysis, and interpretation of numerical data. For example, the manager of a company asked his 36 employees about how many times a day they visited the internet. The number of times the employees visited the web during a day are as follows: 11, 9, 12, 7, 1, 17, 8, 14, 18, 1, 13, 11, 16, 11, 6, 13, 16, 7, 11, 12, 2, 12, 13, 17, 15, 8, 23, 6, 18, 24, 4, 21, 11, 12, 22, 6. The above data can be summarized in a table as follows: Number of VisitsNumber of Employees 1 to 54 6 to to to to

3 Uses of Statistics in Business Quality Control Product Planning Forecasting Yearly Reports Personnel Management Market Research

4 Basic Definitions Draw a subset Describe some characteristic PARAMETER Any VALUE describing a POPULATION STATISTIC Any VALUE describing a SAMPLE VARIABLE Population/Sample CHARACTERISTIC POPULATION ALL ITEMS under study SAMPLE A SUBSET of population Use numerical description Use inference

5 Basic Definitions Population: The set of ALL possible measurements that are of interest. Measurements pertain to a group of people or objects. Examples include (1) ALL students at UNT, (2) ALL students of UNT who own a car, (3) ALL registered voters in the US, (4) ALL production workers at TI, and so on. Two types of population are (1) Finite Population, and (2) Infinite Population. Finite Population: A population of finite items. That is, finite population represents a population whose items can be counted. Examples include (1) ALL individuals in Denton County, (2) ALL registered students of Summer 5W1 at UNT, and so on. Infinite Population: A population of infinite items. That is, an infinite population represents a population whose items can not be counted or are too large to be counted. Examples include (1) ALL fishes in a lake, (2) ALL caribous in Australia, and so on.

6 Basic Definitions Sample: A subset of fraction of the population selected for observation. For example, a group of 50 students out of all students at UNT will comprise a sample. Simple Random Sample: Items in a sample are usually selected at random from the items that comprise the population. Such a sample is called the simple random sample. Census: When a sample consists of the entire population, it is called a census. Variable: Population or sample characteristics that we want to measure. Examples include (1) the height of UNT students, (2) the weight of 100 UNT students, and so on.

7 Basic Definitions Parameter: Any value that describes a population. For example, the number of items in a population is a parameter. Two widely used parameters are (1) Population Size, and (2) Population Mean. Population Size: It refers to the number of items in a population. We use N (big N) to denote population size. If we want to study all diabetic patients in Denton, and say, there are 50 such patients, then the population size is 50 (i.e., N = 50). Population Mean: The average value of all observations in a population. We use μ (pronounced mu) to denote population mean. For example, if the average life expectancy in America is 77.6 years, then the population mean life expectancy in America is 77.6 years.

8 Basic Definitions Statistic: Any value that describes a sample. For example, the number of items in a sample is a statistic. Two widely used statistics are (1) Sample Size, and (2) Sample Mean. Sample Size: It refers to the number of items in a sample. We use n (small n) to denote sample size. If we want to study all diabetic patients in Denton, and say, we randomly select 20 out of 50 such patients, then the sample size is 20 (i.e., n = 20). Sample Mean: The average value of all observations in a sample. We use (pronounced x-bar) to denote sample mean. For example, if the average GPA of a subset of 100 UNT students is 3.75, then the sample mean GPA of that subset of students is 3.75.

9 Levels of Measurements Statistics deals with numerical data collected on a variable or variables. Data collected for a variable involves measurement. Measurement is the assignment of numbers to objects or events of a variable according to a rule. There are four levels of measurements: (1) Nominal Scale (2) Ordinal Scale (3) Interval Scale (4) Ratio Scale

10 Levels of Measurements Nominal Scale Objects are classified into categories or some assigned numbers with no quantitative difference between them. Some examples of variables that use nominal scale include color (red, green, blue, etc.), a country’s international telephone access code (1, 60, 88, and so on), etc. Data collected using nominal scale are called nominal data. Ordinal Scale Objects can be classified into ranked or ordered categories or assigned numbers, but the distances between ranks are not interpretable. For example, we can code educational achievement as 0 = less than H.S., 1 = some H.S., 2 = H.S. degree, 3 = some college, 4 = college degree, and 5=post college. Here, higher number indicates more education. However, the distance from 0 to 1 is not the same as the distance from 3 to 4, and in fact, these distances are not interpretable. Data collected using ordinal scale are called ordinal data.

11 Levels of Measurements Interval Scale Observations can be arranged in order and the differences between any two observations are interpretable (i.e., have meanings). However, interval scale does not include a true zero point, so it is not possible to make statements about how many times higher/lower one observation is than another. An example of interval scale is temperature in Fahrenheit. A 00F does not imply the absence of the temperature. And a difference between 200F and 300F is the same as that between 400F and 500F. However, a temperature of 2000F is not twice as warm as 1000F. Data collected using interval scale are called interval data. Ratio Scale It has all the properties of interval scale plus includes a true zero point. It is possible to make statements about how many times higher/lower one observation is than another. In other words, ratio variables allow us to construct meaningful fractions. An example is the number of customers served by a teller in a bank. Twenty customers served represent twice as many as ten customers served. Data collected using ratio scale are called ratio data

12 Types of Data and Levels of Measurements NUMERICAL DATA Types of Data QUALITATIVE DATA Attributive data QUANTITATIVE DATA Numeric or non-attributive data Levels of Measurements DISCRETE No fraction or decimal. Results from counting. CONTINUOUS Includes fraction. Results from measurement. NOMINAL Objects classified into CATEGORIES ORDINAL Objects classified into ranked CATEGORIES INTERVAL Meaningful differences No true zero point RATIO Properties of Interval Plus true zero point DISCRETE No fraction or decimal. Results from counting.

13 Types of Data and Levels of Measurements Examples of Data The IQ scores of students at UNT. [Quantitative, Discrete, Interval]. Three books on New York Times best sellers list. [Qualitative, Neither Discrete nor Continuous, ordinal]. The weights of 50 randomly selected students. [Quantitative, Continuous, Ratio]. The region of the country you live in. 1) East, 2) West, 3) North, and 4) South. [Qualitative, Neither Discrete nor Continuous, Nominal]. The number of students who graduated from UNT in each of the last five years. [Quantitative, Discrete, Ratio]. Summary of Data and Levels of Measurements: Level of Measurement PropertyNominalOrdinalIntervalRatio Order of data is meaningfulNYYY Difference between data values is meaningfulNNYY Zero point represents total absenceNNNY

14 Two Areas of Statistics Descriptive Statistics Descriptive statistics deals with collection, description and presentation of data. For example, we might draw a graph or crunch a number based on the sample data. Finding the average and constructing a histogram are two examples of descriptive statistics. Inferential Statistics Inferential statistics deals with analyzing the sample data and inferring something about the population. Estimating the average height of all UNT students based on a sample of 50 students is an example of inferential statistics.