Statistics Lecture 1 Notes

7/29/2019 Statistics Lecture 1 Notes

1/5

11

1 - 8

MATH 1050Y

A Non-Calculus Based Introduction toProbability & Statistical Methods

Section A

FW 2012-13

Instructor: Jaclyn Semple

MATH 1050Y-A (FW 2012-13) 1 - 9MATH 1050Y-A (FW 2012-13)

Chapter 1Introduction to Statistics

1-1 Overview

1-2 The Nature of Data

1-3 Uses and Abuses of Statistics

1-4 Design of Experiments

1 -10MATH 1050Y-A (FW 2012-13)

Overview

Polls, studies, surveys and other datacollecting tools collect data from a small partof a larger group so that we can learnsomething about the larger group.

A goal of statistics is to learn about a largegroup by examining data from some of itsmembers.

1 - 11MATH 1050Y-A (FW 2012-13)

Statistics

Statistics is a collection of methods for:

planning experiments & obtaining data

organizing, summarizing, presenting,analyzing, interpreting, and drawingconclusions based on the data

1 -12MATH 1050Y-A (FW 2012-13)

Population and Sample

A population is the complete collection ofall individuals (scores, people,

measurements, and so on) to be studied.

A sample is a subcollection of elementsdrawn from a population.

1 -13MATH 1050Y-A (FW 2012-13)

Parameter and Statistic

Closely related to the concepts ofpopulation and sample are the concepts of

parameterand statistic. A parameter is a numerical measurement

describing some characteristic of apopulation.

A statistic is a numerical measurementdescribing some characteristic of asample.


2/5

22

1 -14MATH 1050Y-A (FW 2012-13)

Parameter

A parameter is a numerical measurementdescribing some characteristic of apopulation.

Example: The 1881 Canada Censusreported that 12.4% of the population ofYale District, British Columbia, belonged tothe Buddhist religion. Assuming that thelist of 8951 residents for the region did notoverlook anyone, then the 12.4% is aparameter.

1 -15MATH 1050Y-A (FW 2012-13)

Statistic

A statistic is a numerical measurementdescribing some characteristic of a

sample. Example: In a survey of 1031 tournament-

level golfers, 44% had the career-threatening condition known as the yips.The figure 44% is a statistic because it isbased on a sample, not the entirepopulation of all professional golfers.

1 -16MATH 1050Y-A (FW 2012-13)

Chapter 1Introduction to Statistics

1-1 Overview

1-2 The Nature of Data

1-3 Uses and Abuses of Statistics

1-4 Design of Experiments

1 -17MATH 1050Y-A (FW 2012-13)

Data

Data are observations (such asmeasurements, genders, surveyresponses) that have been collected.

There are two types of data; quantitativedata and qualitative data.

1 -18MATH 1050Y-A (FW 2012-13)

Quantitative Data

Quantitative data consist of numbersrepresenting counts or measurements.

Examples: The amount of weight that people lose

on a diet program.

The ages of respondents in a survey.

The marks that students get on amidterm exam.

1 -19MATH 1050Y-A (FW 2012-13)

Qualitative Data

Qualitative (or categorical or attribute) datacan be separated into different categories

that are distinguished by some nonnumericcharacteristic.

Examples:

The genders of your classmates.

The colours of cars in a parking lot.

The names of cities in Ontario.


3/5

33

1 -20MATH 1050Y-A (FW 2012-13)

Types of Quantitative Data

Quantitative data can be further dividedinto two types; discrete data and

continuous data.

Quantitative

Discrete Continuous

1 -21MATH 1050Y-A (FW 2012-13)

Discrete Quantitative Data

Discrete data result from either a finitenumber of possible values or a countable

number of possible values. By countable we mean that the possible

values are 0, 1, 2, and so on.

Examples:

The number of eggs laid by chickens.

The number dots that appear when youroll a single die.

1 -22MATH 1050Y-A (FW 2012-13)

Continuous Quantitative Data

Continuous data result from infinitely manypossible values that can be associated withpoints on a continuous scale in such a waythat there are no gaps or interruptions.

Examples:

The heights of your classmates.

The amount of milk produced by cows.

1 -23MATH 1050Y-A (FW 2012-13)

Levels of Measurement

Another way to classify data is to use fourlevels of measurement:

Nominal

Ordinal

Interval

Ratio

1 -24MATH 1050Y-A (FW 2012-13)

Nominal Level of Measurement

The nominal level of measurement ischaracterized by data that consist ofnames, labels, or categories only.

The data cannot be arranged in orderingscheme.

Examples of nominal level data:

Survey responses of yes, no, andundecided.

The colour of peoples eyes.

1 -25MATH 1050Y-A (FW 2012-13)

The ordinal level of measurement involvesdata that may be arrange in some order,but differences between data values either

cannot be determined or are meaningless.

Examples or ordinal level data:

Letter grades of students in a course.

A food critic rates a restaurant asexcellent, good, average, or bad.

Ordinal Level of Measurement


4/5

44

1 -26MATH 1050Y-A (FW 2012-13)

The interval level of measurement is likethe ordinal level, with the additionalproperty that we can determine meaningful

amounts of differences between data.However, there is no inherent zero startingpoint (where none of the quantity ispresent).

Examples of interval level data:

Outdoor temperatures in C.

Years in the Gregorian calendar.

Interval Level of Measurement

1 -27MATH 1050Y-A (FW 2012-13)

The ratio level of measurement is theinterval level modified to include theinherent zero starting point. For values at

this level, differences and ratios are bothmeaningful.

Examples of ratio level data:

The heights of trees in Prince AlbertNational Park.

The prices of university textbooks.

Ratio Level of Measurement

1 -28MATH 1050Y-A (FW 2012-13)

Levels of Measurement

In summary, we have the following fourpossible levels of measurement for data.

Nominal categories with no naturalordering.

Ordinal categories with natural ordering.

Interval differences have meaning butthere is no natural zero.

Ratio differences and ratios have

meaning, and there is a natural zero.

1 -29

Summary of Data & Measurements

Qualitative Quantitative

Numerical NumericalNon numerical

Data

Nominal Ordinal Nominal Ordinal Interval Ratio

MATH 1050Y-A (FW 2012-13)

1 -30

Pause & Practice

MATH 1050Y-A (FW 2012-13)

Determine whether the following examplesgive qualitative or quantitative data? (Ifquantitative, state whether it is discrete or

continuous).

AND

Determine which of the four levels ofmeasurement is most appropriate.(nominal, ordinal, interval, or ratio)

1 -31

Pause & Practice

MATH 1050Y-A (FW 2012-13)

A. Qualitative, nominalB. Qualitative, ordinalC. Quantitative, discrete, ratio

D. Quantitative, discrete, intervalE. Quantitative, continuous, ratio

1. Rating of movies as G, PG and R


5/5

55

1 -32

Pause & Practice

MATH 1050Y-A (FW 2012-13)

A. Qualitative, nominalB. Qualitative, ordinalC. Quantitative, discrete, interval

D. Quantitative, discrete, ratioE. Quantitative, continuous, interval

2. Number of candy bars sold in a fundraiser

1 -33

Pause & Practice

MATH 1050Y-A (FW 2012-13)

A. Qualitative, nominalB. Qualitative, ordinalC. Quantitative, discrete, ratio

D. Quantitative, continuous, ratioE. Quantitative, continuous, interval

3. The time it takes a student to drive tocollege

1 -34

Pause & Practice

MATH 1050Y-A (FW 2012-13)

A. Qualitative, ordinalB. Quantitative, discrete, ratioC. Quantitative, discrete, intervalD. Quantitative, continuous, ratioE. Quantitative, continuous, interval

4. Temperatures of Haliburton lake at variouslocations on its surface.

1 -35

Coming up

MATH 1050Y-A (FW 2012-13)

Our main aim for the next few weeks willbe to summarize and describequantitative data

Assignment #1 will be posted on Monday Due Sept. 18th in seminar

For next class: Read section 1-3 & 1-4

Documents

Statistics Lecture 1 Notes