Statistics Exam 1

(ch 1-4)

The science of collecting, organizing, presenting, analyzing, and interpreting data to assist in making more effective decisions.

Statistics

2 types of Statistics

descriptive and inferential

…can be used to organize data into a meaningful form

Descriptive statistics

Methods of organizing, summarizing, and presenting data in an informative way.

descriptive statistics

The methods used to estimate a property of a population on the basis of a sample.

inferential statistics

The entire set of individuals or objects of interest or the measurements obtained from all individuals or objects of interest.

population

A portion or part of the population of interest.

sample

There are two basic types of variables

qualitative variable and quantitative variable

An object or individual is observed and recorded as a non-numeric characteristic or attribute. Examples: gender, state of birth, eye color

qualitative variable

A variable that is reported numerically.

Examples: balance in your checking account, the life of a car battery, the number of people employed by a company

quantitative variable

…variables can be discrete or continuous

Quantitative variables

….variables are typically the result of counting

-Examples: the number of bedrooms in a house (1, 2, 3, 4, etc.), the number of students in a statistics course (326, 421, etc.)

Discrete variables

…variables are usually the result of measuring something. Can assume any value within a specific range

- Examples: Duration of flights from Orlando to San Diego (5.25 hours), grade point average (3.258)

continuous

There are four levels of measurement

Nominal, ordinal, interval, and ratio

The level of measurement determines the type of …

statistical analysis that can be performed

… is the lowest level of measurement. Because it provides the least amount of information compared to the other levels.

nominal

Data recorded at the … level of measurement is represented as labels or names. They have no order. They can only be classified and counted.

-Examples: classifying M&M candies by color, identifying students at a football game by gender

nominal

…adds ranking (e.g., small, medium, large)

-The rankings are known, but not the magnitude of differences between groups

ordinal

Data recorded at the … level of measurement is based on a relative ranking or rating of items based on a defined attribute or qualitative variable. Variables based on this level of measurement are only ranked and counted.

-Examples: the list of top ten states for best business climate, student ratings of professors

ordinal

-This data has all the characteristics of ordinal level data, plus the differences between the values are meaningful

-There is no natural 0 point; a zero does not represent the absence of the condition

interval level

For data recorded at the … level of measurement, the … or the distance between values is meaningful. The … level of measurement is based on a scale with a known unit of measurement.

-Examples: the Fahrenheit temperature scale, credit scores (300- 850), SAT scores (400-1600)

interval

The data has all the characteristics of the interval scale, and … between numbers are meaningful -The 0 point represents the absence of the characteristic

ratio

Data recorded at the … level of measurement are based on a scale with a known unit of measurement and a meaningful interpretation of zero on the scale.

-Additionally, these variables have zero measurements representing a lack of the attribute. For example, zero kilograms indicates a lack of weight. • Examples: wages, changes in stock prices, and height

ratio

Practice … with integrity and honesty when collecting, organizing, summarizing, analyzing, and interpreting numerical information

statistics

… is used to process and analyze data and information to support a story or narrative of a company

Business Analytics

chapter 2 is next

chapter 2 is next

… A grouping of qualitative and quantitative data into mutually exclusive and collectively exhaustive classes showing the number of observations in each class.

frequency table

Each observation is in only one class.

mutually exclusive

There is a class for each value

Collectively exhaustive

Constructing Frequency Tables

1. Sort the data into classes

2. Count the number in each class

3. Report as the class frequency

-Example: Car sales by location

…is just a tally of how many times something happened.

a frequency

…tells you how significant that number is compared to the entire group.

relative frequency

to find …take the class frequency and divide by the total number of observations.

relative frequencies

Pro-tip: In a Relative Frequency table, the sum of the relative frequency column should always equal … If it doesn't, someone missed a car!

1.00 (or 100%)

…A graph that shows the qualitative classes on the horizontal axis and the class frequencies on the vertical axis.

bar chart

the bar chart is the most common graphic to present a…

qualitative variable

…is class with the highest frequency

the mode

A chart that shows the proportion or percentage that each class represents of the total number of frequencies

pie chart

A grouping of quantitative and qualitative data into mutually exclusive and collectively exhaustive classes showing the number of observations in each class

-shows the pattern and the peaks and the gaps

-describes the pattern

frequency distribution

A graph in which the quantitative classes are marked on the horizontal axis and the class frequencies on the vertical axis.

histogram

Consists of line segments connecting the points formed by connecting the class midpoints.

Gives a quick picture of the main characteristics of the data.

Good to use when comparing two or more distributions.

frequency polygon

Add each frequency to the frequencies before it

Cumulative frequency distribution

Divide the cumulative frequencies by the total number of observations

Cumulative relative frequency distribution

chapter 3 is next

chapter 3 is next

A measure of …is a value used to describe the central tendency of a set of data.

location

Common measures of location:

Mean

Median

Mode

The …is the most widely reported measure of location

arithmetic mean

The mean is both a …

population parameter and sample statistic

-An interval or ratio scale of measurement is required

-All the data values are used in the calculation

-The .. is unique

-The sum of the deviations from the … equals zero

-A weakness of the … is that it is affected by extreme values

(large or small).

sample mean

For data containing extreme values, the .. may not

fairly represent the central location

mean

The midpoint of the values after they have

been ordered from the minimum to the maximum

values

median

-The … is the value in the middle of a set of ordered

data.

-At least the ordinal scale of measurement is required.

-Because you need a meaningful ranking of the data values

to define what the “middle” is

-Extreme values do not influence it.

-Fifty percent of the observations are larger than the

...

-Fifty percent of the observations are smaller than the

….

-It is unique to a set of data.

median

The value of the observation that occurs most

frequently

mode

The … can be found for nominal level data. The mode is

meaningful because you can still say which category occurs

most often

-A set of data can have more than one ....

- set of data could have no ...

mode

-The .. is found by multiplying each observation

by its corresponding weight.

-A convenient way to compute the mean when there are

several observations with the same value.

weighted mean

measures of location only describe the center, so we need… to see how scattered the data is sat at the center

dispersion

Measures of dispersion include:

-Range.

-Variance.

-Standard Deviation.

The simplest measure of dispersion is…

range

=max value - min value

range

range is influenced by…

extreme values

The variance measures how much the values vary from their ….

mean

The … is used to compare the spread of two or more sets of observations

-finds the square root of variance
Small: The values are close to the mean

Large: The values are widely scattered about the mean

standard deviation

is for any set of values regardless of the shape of the distribution

-one size fits all

-use if the problem says unknown distribution

Chebyshev’s theorem

The Empirical Rule or Normal Rule provides an approximation.

-symmetric,bell-shaped curve

-use if problem says normally distributed

• 1 standard deviation of the mean: about …of values.

• 2 standard deviations of the mean: about … of values.

• 3 standard deviations of the mean: about … of values.

68
95
99

chapter 4 is next

chapter 4 is next

Summarizes the distribution of one variable by stacking dots as points on a number line that shows all the values.
-If there are identical values, the dots are “piled” on top of each other.

dot plot

-The standard deviation is the most widely used measure of

dispersion.

-We can also determine the location of values that divide a

set of observations into parts.

quartiles

Q1=
Q2=
Q3=

25
50 (median)
75

Divide a set of observations into 10 equal parts

deciles

Divide a set of observations into 100 equal parts

percentiles

Excludes the minimum and maximum when calculating quartiles

-10-20, 20-30, 30-40

exclusive method

Includes the minimum (0th percentile) and maximum

-10-19, 20-29, 30-39

(100th percentile) when calculating quartiles.

Formula for the position of the pth percentile:

inclusive method

…A graphic display that shows the general shape

of a variable’s distribution.

-It is based on five descriptive statistics: the maximum and

minimum values, the first and third quartiles, and the

median

box plot

A data point that is unusually far from the other

outlier

four common skewness shapes

symmetric
positively skewed
negatively skewed
bimodal

-The median is roughly centered in the box

-the whiskers (lines extending from the box) are about the

same length

-Q1 → Median → Q3 are evenly spaced.

Symmetric Distribution

-The median is closer to Q1

-The right whisker (upper tail) is longer

-Q3 – Median > Median – Q1

Right-Skewed Distribution (Positively

Skewed)

-The median is closer to Q3

-The left whisker (lower tail) is longer

-Q1 – Median > Median – Q3

Left-Skewed Distribution (Negatively

Skewed)

Graphical technique used to show the relationship between two variables measured with interval or ratio scales

-we use to see if two different things are related (correlation)

scatter diagram

…Measures the direction and strength of the relationship

-Ranges from −1.0 to +1.0

-The closer the coefficient is to −1.0 or +1.0, the stronger the

relationship

-If r is close to 0.0, we can say that there is no relationship between the variables

-Positive indicates a positive relationship

-Negative indicates a negative relationship

Correlation coefficient

…A table used to classify observations according to two identifiable

characteristics

-It is a cross-tabulation that simultaneously summarizes two variables of interest

-Both variables need only be nominal or ordinal

contingency table