1 - heatherchafe

1.1 Definitions 1.1.1 Define the terms: statistics, data, population, and sample. Statistics refers to the science of collecting, organizing, presenting,
analyzing, and interpreting data to assist in making more effective
decisions. Data are measurements of one or more variables of a sample which was drawn
from a population. A population is the complete collection of elements (scores, people,
measurements) in which we want to study A sample is a set of individual elements (again scores, people,
measurements...) taken from a population. 1.2 Type of Statistics 1.2.1 Describe the difference between descriptive and inferential
statistics The study of Statistics (as will the chapters of our textbook) can be
broken down into two main types: Descriptive Statistics and Inferential
Statistics.
Descriptive Statistics usually utilizes graphs, charts, tables, or
calculations to describe data. On your income tax brochure, there is
usually a pie chart which shows the breakdown of your tax dollar. It
clearly identifies where your hard earned dollar goes.
The other type is known as Inferential Statistics and this usually is
utilized when making a statement, reaching a decision, or coming to some
conclusions. An example would be when the local chip truck wants to trial
test a new brand of crispy fries. A sample of the loyal customers might be
given the new chips and their responses to its tastiness and marketability
would give the owners sufficient information for launching the newer and
better chips!
In summary, descriptive statistics are methods of organizing, summarizing,
and presenting data in an informative way whereas inferential statistics
can be a decision, an estimate, a prediction, or a generalization about a
population, based on a sample. 1.2.2 Identify the four types of data and the characteristics of each type. Data are measurements of one or more variables of a sample which was drawn
from a population. This data can be classified into four types: nominal,
ordinal, interval, or ratio. Types of Data:
Nominal data, as the name suggests, is essentially when the researcher puts
a name to his or her observations. Warranty cards and surveys often ask one
to check the box that best describes, say, one's profession. The list may
include secretarial; professional; skilled trade. In such a case it is
clear that we are simply naming data. Confusion may creep in however when
we use numbers as names. For instance, if we were comparing the performance
of men and women on some task, we might for ease of computation refer to
all men as 0 and all women as 1. Such numbers are still really just names,
however, and would have no more computational value than the simple label
men or women.
Ordinal data is essentially the same as nominal data, but in this case the
data may meaningfully be arranged in order: for instance tall, medium,
short. A psychologist may want to rank children in a class on the basis of
how skilled they are at reading. The resultant data will tell us who is the
best reader, who is the second best, and so on, but gives us no information
on how much the children differ from each other in terms of reading skill.
Interval data is perhaps the most commonly-collected type of data in
Psychology. In interval data, the difference between any two adjacent
numbers is equal to the difference between any other two adjacent numbers.
In other words, an interval scale allows one to measure differences in size
or magnitude. This may seem a confusing concept, but bear in mind that the
IQ scale, for instance, is an interval scale. If we say that Jim scores 120
on an IQ test, and Tom 90, we can say that Jim's score is 30 points higher.
We know that Jim's score is the greater of the two, and we know by how much
it is greater. However it is not possible to say that Jim is one-third more
intelligent than Tom. This is because the IQ scale has no really meaningful
absolute zero point.
Ratio data contains all of the attributes of interval data, but includes in
addition an absolute zero point. A good example is scores in an exam.
Because of the properties of the ratio scale, if Jim scores 100 in a test
and Tom 50, we may meaningfully say that Jim has scored twice as highly as
Tom.
Note: Qualitative (or categorical) Data are non numerical data which
includes nominal and ordinal data.
Quantitative (or numerical) Data are numerical data which includes interval
and ratio data.
2.0 Descriptive Statistics
2.1 Discuss what is meant by a frequency distribution.
Frequency Distributions:
Sometimes we need to reduce a large set of data into a much smaller set of
numbers that can be more easily comprehended. Lets take for example if you
have recorded the population sizes of 500 randomly selected cities, there
is no easy way to examine these 500 numbers visually and learn anything.
It would be easier to examine a condensed version of this set of data and
this is where the frequency distribution comes into play.
Hence, a frequency distribution is a grouping of data into mutually
exclusive classes showing the number of observations in each.
Lets look at an example of a frequency distribution:
|Class number |Number of dolls sold |frequency |
|1 |5000 up to 10000 |1 |
|2 |10000 up to 15000 |5 |
|3 |15000 up to 20000 |2 |
|4 |20000 up to 25000 |2 |
|5 |25000 up to 30000 |6 |
|6 |30000 up to 35000 |4 |
|7 |35000 up to 40000 |9 |
|8 |40000 up to 45000 |8 |
|9 |45000 up to 50000 |4 |
|10 |50000 up to 55000 |7 | This frequency distribution describes the number of dolls sold by a group
of companies. For example, you can see that 1 company sold between 5000 and
10000 dolls, 5 companies sold between 10000 and 15000 dolls, etc. How many companies are there in total represented in the frequency
distribution? 1+5+2+2+6+4+9+8+4+7= 48 companies. If a company sells 10000 dolls exactly, which class would it be counted
under? It would be counted in the 10000 up to 15000 class NOT the 5000 up to 10000
class. 2.1.2 Define the terms: frequency, relative frequency, classes and class
limits frequency: how often something happens (count the number of times) class: how the data is split up (For example, the data above is split up
into 10 classes) class limits: Class limits are the highest and lowest values in a
particular class . For example in class number 2 above the lower class
limit is 10000 and the upper class limit is 15000. relative frequency: Relative class frequency is the percentage (given in
decimal form) of the data values which lie in each class. i.e. relative frequency= frequency of a given class___
total number of values in the data
example#1: What is the relative frequency of class #3? example#2: What is the relative frequency of class#7? **2.1.3 Constructing a frequency distribution When you are given data(a bunch of numbers) and you are asked to construct
a frequency diagram there are certain steps you need to take. The following example will illustrate. Construct a frequency diagram for the following data on prices of vacation
packages to Europe. Data for prices of European vacation packages: 2599 4580 9945 2100
3800 5379 899 999
9720 5299 5208 7399
4200 3349 3800 3557
1200 2470 1199 2200
9366 3855 5399 6899
8255 1200 2100 9999
Steps: 1. Determine the number of classes (intervals) to use. (i.e. how to split
the data up) This requires judgment. It is best to have between
________________ classes. (10 is usually good)
2. Come up with the class width. (CS) using the following equation: (Tip! To make your frequency distribution easier to interpret, it is good
to round to the nearest ten, hundred, thousand, etc) Note: This will cause
the number of classes to change but not by much. 3. Make sure the lowest class contains the lowest data value and begin with
a value that makes the frequency distribution easy to interpret. In our
case the lowest class must include 899, so the first class could be 0-900.
It doesn't have to start at 0 though. We could have picked 100-1000 or 200-
1100 for our first class. The frequency distribution for the data given above:
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| | | 2.1.4 Construct a relative frequency distribution Example: Use the frequency distribution constructed above in 2.1.3, and
turn it into a relative frequency distribution. Steps: Step 1: Do a frequency distribution. Step 2: Calculate the relative frequency for each class and put this info
into a new column called "relative fre