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Summary - Statistics for Business and Economics, Chapter 1, 2, 7 - 16 (Course: Statistics II)
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Summary of the book Statistics for Business and Economics, Chapter 1, 2, 7 - 16. Course: Statistics II
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Chapter 1, 2, 7-16
Chapter 1
1.1. Decision making in an uncertain environment
- Population: complete set of all items that interest an investigator.
- Sample: observed subset/portion of a population with sample size n.
- Simple random sampling / random sample: procedure used to select a sample of n
objects from a population in such a way that each member of the population is
chosen by chance, the selection of one member does not influence the selection of
any other member, each member of the population is equally likely to be chosen and
every possible sample has the same chance of selection.
- Systematic sampling: selection of every jth item in the population; population list is
arranged in some fashion unconnected with the subject of interest. j = N/n.
- Parameter: numerical measure, describes a specific characteristic of a population.
- Statistic: numerical measure, describes a specific characteristic of a sample.
- Sampling error: results from the fact that information is available on only a subset of
all the population members.
- Nonsampling errors: error unconnected with the kind of sampling procedure used.
- Descriptive statistics: focus on graphical and numerical procedures that are used to
summarize and process data.
- Inferential statistics: focus on using the data to make predictions, forecasts and
estimates to make better decisions.
1.2. Classification of variables
- Categorical variables: produce responses that belong to groups or categories.
- Numerical variable:
o Discrete numerical variable: may have a finite number of values, response
that comes from a counting process.
o Continuous numerical variable: may take any value within a given range of
real numbers, usually arises from measurement, not counting.
- Qualitative data: no measurable meaning to the difference in numbers.
o Nominal data: words that describe the categories/classes of response.
Numbers have no meaning other than for categorizing; 1. Yes, 2. No.
o Ordinal data: rank the ordering of items; 1. Poor, 2. Average, 3. Good.
- Quantitative data: measurable meaning to the difference in numbers.
o Interval scale: indicates rank and distance from an arbitrary zero measured in
unit intervals; temperature.
o Ratio data: indicate both rank and distance from a natural zero, with ratios of
two measures having meaning; weight, age.
1.3. Graphs to describe categorical variables
- Frequency distribution: left column (classes/groups) includes all possible responses,
right column is a list of frequency.
1
, - Relative frequency distribution: dividing each frequency by the number of
observation and multiplying the resulting proportion by 100%.
- Bar chart: describes categorical data, frequency of each category.
- Pie chart: describes categorical data, proportion of frequencies in each category.
- Cross table: lists number of observations for every combination of values for two
categorical or ordinal variables.
- Pareto diagram: bar chart that displays the frequency of defect causes. The bar at
the left indicates the most frequent cause. Used to separate the vital few from trivial
many.
1.5. Graphs to describe time-series data
- Time series: set of measurements, ordered over time, on a particular quantity of
interest. Sequence of observations is important.
- Line chart / time-series plot: series of data plotted at various time intervals.
1.6. Graphs to describe numerical variables
- Frequency distribution for numerical data: table that summarizes data by listing the
classes in the left column and the number of observations in the right column.
- Construction of a frequency distribution:
1. Determine k, the number of classes.
2. Classes should be the same width, w, which is determined by the following:
largest observation−smallest observation
w = class width =
number of classes
3. Classes must be inclusive and nonoverlapping.
- Cumulative frequency distribution: contains the total number of observations
whose values are less than the upper limit for each class. Frequencies of all
frequency distribution classes are added up to the present class.
- Relative cumulative frequency distribution: cumulative frequencies can be
expressed as cumulative proportions or percents.
- Histogram: graph that consists of vertical bars constructed on a horizontal line that is
marked off with intervals for the variable being displayed.
- Ogive / cumulative line graph: line that connects points that are the cumulative
percent of observations below the upper limit of each interval in a cumulative
frequency distribution.
- Symmetry: observations are balanced or approximately evenly distributed.
- Skewness: observations are not symmetrically distributed.
- Stem-and-leaf display: data are grouped according to their leading digits and the
final digits are listed separately for each member of a class.
- Scatter plot: locating one point for each pair of two variables that represent an
observation in the data set.
1.7. Data presentation errors
- Misleading histograms: interval widths are not always the same.
- Misleading time-series plots: by selecting a particular scale of measurement, an
impression can be created either of relative stability or substantial fluctuation.
Chapter 2
2
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