What is statistics

1
What is statistics

• Statistical training is necessary and important
  for many reasons. In almost any area of work, you
  must be able to read, interpret, and apply the
  results of a statistical analysis of research
  data.
•  
• What is Statistics all about? Statistics
  involves the collection, organization,
  interpretation and presentation of data.
• Studying statistics will help you to understand
  the information and to reach correct conclusion.

2
Example 1.1 The nutrition chart (of sandwich) in
McDonalds menu
3
Chapter 1 Population and Sample

• An experiment unit(or subject) is the smallest
  entity that is of interest in a statistical
  study.
• A variable is any characteristics that can be
  measured on each experiment unit in a statistical
  study.
• An observation is a value that the variable
  assumes for a single unit.
• The collection of observations assumed by the
  variables in the study is called a data set.
• For example 1.1
• experiment unit A McDonalds item
• Variables calories, protein, carbohydrates,
  total fat, saturated fat,
  cholesterol, and sodium
• Population all the items in the McDonalds menu

4

• The population is the collection of all objects
  or items that are of interest in a statistical
  study. The individual objects in the population
  are the experimental units or subjects.
• A sample is a finite portion (subset) of the
  population that is used to study the
  characteristics of concern in the population. The
  number of objects in this sample is called sample
  size.
• Bias is a systematic tendency of the sample to
  misrepresent the population
• A simple random sample (s.r.s) of size n consists
  of n elements chosen from the population in such
  a way that all samples of that size have the same
  chance of being selected

5
For example, (the lottery sampling)

• 100 balls are mixed thoroughly in a bag. draw 10
  balls randomly from the bag. Try twice
  with/without replacement.

6

• Example1.2 Now we are interested in the heights
  of MSU students. We measured the heights (and/or
  weight, gender) of all the students and recorded
  as follows X1, X2,. Randomly select 50
  students to measure their heights. Explain the
  concepts above.
• Population
• All MSU students
• Experiment unit
• A MSU student
• variables
• height,( and/or weight, gender)
• Observations
• any one of X1,X2,.
• Data set
• X1,X2,.
• Sample
• the 50 selected students

7

• A Census is a sample consisting of the entire
  population.  
• Why dont we always do a census?
• Time time consuming,
• Cost cost more,
• Inaccessible population units study all the
  sunfish in Lake Michigan, say.
• Destructive testing destroy the unit

8
Statistics terms

• experimental unit, subject
• variable
• population
• sample
• census
• s r s simple random sample

9
Exercise 1.1

• A stock market investor is interested in oil
  stocks.She collects last years price/earnings
  ratios on ten randomly selected oil stocks. The
  data of ratios are X1,X2,, X10.
• What is our population?
• What is the variable? Give one observation.
• What is our sample and sample size?
• What is our data set?

10
Exercise1.2

• Want to know the average height of 2nd grade
  students in East Lansing Public schools. Instead
  of measure all 2nd grade students, we sample the
  60 2nd grade students randomly, The data of
  heights are X1,X2,, X60.
• What is our population?
• What is the variable? Give one observation.
• What is our sample and sample size?
• What is our data set?

11
Chapter 2 Univariate DataData set for seven
undergraduate students (table 2.1)
12
Data Sets

• A univariate data set is a data set in which one
  measurement (variable) has been made on each
  experiment unit.
• A bivariate data set is a data set in which two
  measurements (variables) have been made on each
  experiment unit.
• A multivariate data set is a data set in which
  several measurements (variables) have been made
  on each experiment unit.

13
Types of Variables

• A categorical variable (also called a qualitative
  variable) is a variable whose values are
  classifications or categories.
• For example, Gender Male, Female
• Occupation Student, doctor,
  teacher,

14

• A Numerical variable (also called a quantitative
  or measure variable) is a variable whose values
  are numbers obtained by a count or measurement.
  For example weight, height.
• 1. A discrete variable is a numerical variable
  that can assume a finite number or at most a
  countable infinite number
• 2. A continuous variable is a numerical
  variable that can take any number on an interval
  of the real number line. For example, height,
  weight.

15
Remark

• Coding of categorical variable does not make it
  numerical.
• For example Gender
• Male -- 0 Female -- 1

16
Types of Data
Discrete Can only take on certain values in an
interval.
Numerical (Quantitative)
Continuous Can take on infinitely many values
in an interval.
Categorical (Qualitative)
17
Exercise 2.1 Classify the following as
categorical or numerical (discrete or
continuous).

• a. Age of freshmen in MSU
• b. Faculty rank
• c. Weight of newborn babies
• d. Murder rate in a major city
• e. Number of children in a family
• f. Brand of television set

18
display categorical variable

• frequency table
• bar chart bar graph
• pie chart

19
Frequency table

• A table that lists the different categories of
  categorical data and the corresponding
  frequencies (relative frequencies) with which
  they occur
• A class is one of the categories into which that
• the qualitative data is classified.
• Class frequency is the number of observations in
  each class.
• Class relative frequency is the class frequency
  divided by the total number of observations.
  (observations in each class)

20
Example2.2 Time/CNN telephone poll of 500 adult
Americans Has the amount of crime in your
community increased in the past 5 years?

21
Bar Chart

• is a picture consisting of horizontal and
  vertical axis with rectangles that represent the
  frequency (relative frequency) of the categories
  of a variable.

22
Bar chart of CNN telephone poll
23
Pie Chart

• A circle or pie is divided into pieces
  corresponding to the categories of the variable
  so that the size of the slice is proportional to
  the relative frequency of the category.

24
Pie Chart
25
Exercise 2.3 Sampling 100 students from MSU
students to get their level information, here are
the data Fr 12, So 24, Jr 32, Sr 24, Gr 8.draw
bar chart of the sample data
26
Display numerical variable

• Example 2.3 The cholesterol levels from a sample
  of 62 subjects from the Framingham Heart study
• 393 353 334 336 327 300 300 308 283 285
  270 270 272
• 278 278 263 264 267 267 267 268 254 254
  254 256 256
• 258 240 243 246 247 248 230 230 230 230
  231 232 232
• 232 234 234 236 236 238 220 225 225 226
  210 211 212
• 215 216 217 218 200 202 192 198 184 167
  

27
Display numerical variable

• dot plot ok for small data set
• stem leaf
• Grouped frequency table
• histogram

28
Example 2.4

• A psychologist wishes to test a new method to
  improve rote memorization by college students. A
  sample of 20 college students were taught by this
  method and then asked to memorize a list of 100
  word phrases. The following numbers of correct
  word phrases were recorded for the 20 students.
• 84 59 82 78 74 96 44 76 85 66
• 77 91 62 54 72 65 84 38 76 70

29
Dotplot
84 59 82 78 74 96 44 76 85 66 77 91
62 54 72 65 84 38 76 70

• Distribution of a variable specifies the distinct
  values that the variable assumes and how often
  these values occur.

30
Stem and leaf Plot

• 84 59 82 78 74 96 44 76 85 66
• 91 62 54 72 65 84 38 76 70
• Step 1.Chose one leading digit as stem, the
  trailing digit or digits as leaves

31
Stem and leaf Plot.

• 84 59 82 78 74 96 44 76 85 66
  
• 77 91 62 54 72 65 84 38 76 70
• Step2. List the stem in a column and record the
  leaves
• 3
• 4
• 5
• 6
• 7
• 8 4
• 9

32

• 84 59 82 78 74 96 44 76 85 66
• 77 91 62 54 72 65 84 38 76 70
• Step3. Fill stem and leaf plot
• 3 8
• 4 4
• 5 9 4
• 6 6 2 5
• 7 8 4 6 7 2 6 0
• 8 4 2 5 4
• 9 6 1

33

• 84 59 82 78 74 96 44 76 85 66
  
• 77 91 62 54 72 65 84 38 76 70
• Step4. Reorder the leaves of each stem
• 3 8
• 4 4
• 5 4 9
• 6 2 5 6
• 7 0 2 4 6 6 7 8
• 8 2 4 4 5
• 9 1 6
• Step5Indicate the units for stem and leaf

34
Example 2.5

• The following is the concentration of mercury in
  25 lake trout caught in a major lake
• 2.2 3.4 3.0 2.6 3.8 1.8 2.8 3.2
  3.7
• 1.4 2.7 3.6 1.9 2.2 3.0 3.3 2.3
• 1.7 2.6 3.5 3.0 2.9 3.4 3.1 2.4
• Exercise create a stem leaf plot for this data.

35
Stem and leaf plot

• 1 4 7 8 9
• 2 2 2 3 4 6 6 7 8 9
• 3 0 0 0 1 2 3 4 4 5 6 7 8
• Unit of leaf .1

36
double-stem stem and leaf plot

• 1 4
• 1 8 9 7
• 2 2 3 4
• 2 6 8 7 6 9
• 3 4 0 2 0 3 0 4 1
• 3 8 7 6 5

37
Ordered double-stem stem and leaf plot

• 1 4
• 1 7 8 9
• 2 2 3 4
• 2 6 6 7 8 9
• 3 0 0 0 1 2 3 4 4
• 3 5 6 7 8