Qmb stacey brook

Dataset

all the data collected for a particular analysis

Data

The facts & figures collected, analyzed, and summarized for presentation and interpretation.

Element

The entity on which data is collected.

Variable

a characteristic of interest of an element.

Observation

The variables associated with an individual element.

Categorical Data

Use numeric or ordinal values of measurement of categories.

Quantitative Data

use numeric (quantitative) measures

Cross-sectional Data

data collected at a similar point in

time.

Time Series

data collected over several time periods.

Panel Data

combination of cross-sectional and time series data.

Descriptive Statistics

Describes data or variables

Population

Is the set of all data/variables of a statistical analysis.

Sample

is a subset of the population

Statistical Inference:

Uses data from a sample to make estimates and test hypothesis about the characteristics of a population.

What does row 1 usually contain in Excel?

Typically row 1 contains the variable's names.

What does Column A usually contain in Excel?

Column A contains the elements; and the rest of the

worksheet contains the data in the dataset.

How do you calculate the mean in excel?

=Average

How do you calculate the median in excel?

=median

What is data analytics?

Analytics is the scientific process of transforming data

for decision making. There are three broad areas of

data analytics.

Descriptive Analytics

describe what hashappened in the past.

Predictive Analytics

uses statistical models from

past data to predict the future [forecasting] or access

the impact of one variable on another [inference].

Prescriptive Analytics

uses models seeking to find a best (optimal) solution. Often these are sometype of optimization model.

The difference between data and big data are

We will use data (not big data)

1. Volume - the number of observations.

2. Velocity - the speed at which data is collected.

3. Variety - the forms of data are of different types.

4. Veracity - the reliability of the data generated.

Data Mining

Focuses on extracting predictive information from big

data.

Frequency Distribution

a tabular summary of datashowing the number (i.e. frequency) of observationsin each of several non over-lapping categories.

Relative Frequency

frequency of a class/ n of a class

Percent Frequency

relative frequency x 100

Bar Chart:

a visual display of frequency; relative

frequency & percent frequency distributions.

How would you make a frequency table in excel?

a. Select any cell in Column A

b. Click Insert on the Ribbon Tab

c. In Tables, click Recommend Pivot Tables

d. Click OK.

pie chart

a visual display of frequency; relative frequency & percent frequency distributions.

How would you create a bar chart in excel?

a. Select any cell from A1 to A51.

b. Click the Insert tab from the Ribbon.

c. In Charts, click Recommended Charts

d. Click OK. [bar chart appears in a new worksheet]

What are the basic steps to using excel?

Access the data, Functions & formulas, Apply tools, Editing options

A frequency distribution with quantitative data mustdefine the classes for a frequency distribution by:

a. determine the number of non over-lapping

classes;

b. determine the width of each class;

c. determine the class limits.

Number of Classes

Typically, between 5 and 20. Small datasets have less; larger datasets have more.

Width of the Class

Generally, it should be the same for each class. Approximate class width = (largest data value - smallest data value)/number of classes.

Class Limits

Each data observation must only belong to one class.

Relative Frequency Distributions

frequency of theclass/n

To construct a frequency distribution in excel

we must group the rows.

What if a class has no data?

[Excel automaticallyremoves these classes]

To change this:Click the Layout and Print tab

Choose show items with no data; click OK

Histogram

A visual display of a frequency, relative frequency, or percent frequency distribution, where the variable of interest is on the horizontal axis and the frequency, relative frequency, or percent frequency is on the vertical axis.

A histogram shows

A histogram shows the shape of the distribution of

the variable of interest.

A distribution is skewed if more of the data is either

to the left or right of the distribution.

How would we construct a histogram in excel?

a. Select any cell in the pivot table report (A3:B9)

b. Click Insert on the Ribbon.

c. In the Charts group, click Recommended

Charts

d. Click OK.

set the gap width to 0

Cumulative Distributions

Presents the number of data items with values less than or equal to the upper-class limit for each class

cumulative relative frequency distribution

A cumulative relative frequency distribution shows the proportion of data items with values less than or equal to the upper limit of each class.

cumulative percent frequency distribution

A cumulative percent frequency distribution shows the percentage of data items with values less than or equal to the upper limit of each class.

Crosstabulation:

a tabular summary of data for twovariables (either categorical or quantitative)

EX: Suppose we have data from a sample of 300

restaurants on overall quality and the meal price.

(This allows us to see if there is a pattern the two

variables).

Scatter Diagram & Trendline:

a scatter diagram is agraphical display of the relationship between twoquantitative variables and a trendline provides anapproximation (i.e. an estimate) of the relationship;which can be positive, negative or none.

How would you create a scatter diagram in excel?

a. Select cells B1:C11.

b. Click Insert on the Ribbon.

c. In the Charts group, click Insert Scatter (X,Y) or

Bubble chart (or Recommended Chart)

d. When the list of scatter subtypes appears, click

scatter.

e. In chart elements- Select the checkbox for Trendline.

Side-by-Side & Stacked Bar Charts

These are extensions of a basic bar chart as they are

used to display and compare two variables.

stacked bar chart

A stacked bar chart has one bar broken into

segments of a different color showing the relative

frequency of each class.

Side by side bar chart

A side-by-side bar chart depicts multiple bar charts

on the same display.

How would we construct a side by side bar chart in excel?

c. In the Charts group, click recommended charts

(preview)

d. Click OK

Mean (or average):

is the average value for a variable and the sample mean is denoted as ̅ 𝑥, and the population mean is denoted as 𝜇.

Σ

The Sum symbol

𝑥𝑖 (x sub i)

a piece of data in the data set

EX:12345- 4=xi

n and N

n is the number of observations in a sample

N is the number of observations in a population

Median

is the value in the middle, when the data are

arranged in ascending order. When the number of

observations are odd the median is the middle value;

when the number of observations are even the

median is the average of the two middle values. The

median avoid problems where there are extreme

high or low values for x.

Mode

Mode is the value that occurs with the greatest frequency. If there are two values that are most frequent the variable is bi-modal; if there are more then it's multi-modal.

How would we calculate mode in excel?

=mode.sngl

Weighted Mean:

used when observations have different weights (relative importance).

Geometric Mean:

is a measure of location by finding the nth root of the product of n values.

How would we calculate geometric mean in excel?

=geomean

Percentile:

provides information about how the data

is spread over the interval from the smallest to the

largest value. The pth percentile divides the data into

two parts - approximately p% of the observations are

less than the pth percentile and approx. (100-p)% are

greater.

Quartiles:

represent how the data is spread over four

parts, each containing approximately 25% of the

observations. Q1 is the first quartile (25th percentile);

Q2 = second quartile (50th percentile or median); Q3 =

third quartile (75th percentile).

How would we calculate percentile in excel?

=percentile.exc(B2:B13,k)

A percentile calculated with . 4 as k means 40% percent of values are less than or equal to the calculated result

How would we calculate quartiles in excel?

= quartile.exc(B2:B13,quartile number)

You would select either 1, 2,3, or 4 depending on which quartile you would like to know.

These are measures of variability or dispersion of the data.

Range: largest value and smallest value.

Interquartile Range: Q 3 - Q 1 , is the range of the

middle 50% of the data.

Variance:

measures variability using all the data, based on the difference between the value of xi and the mean. This difference is called a deviation from the mean.

Variance:

The population variance: 𝜎^ 2

The sample variance: 𝑠^2

The benefit is that it is useful in comparing the

variability of two or more variables; but one difficulty

is the units, since the variance is in units squared.

Standard Deviation:

The population standard deviation: 𝜎= Sqrt. of 𝜎^2

The sample standard deviation: 𝑠= Sqrt. of 𝑠^2

The advantage is now the units are no longer

squared, making it easier to compare the results to

the mean as well as other statistics.

How would we calculate Variance for a sample in excel?

=var.s(

How would we calculate standard deviation for a sample in excel?

=stdev.s(

Coefficient of Variation

This is a measure of how large the standard deviationis relative to the mean.

How to use descriptive statistics in excel:

a. Click on Data in the Ribbon.

b. Under Analysis, click on Data Analysis.

c. Choose Descriptive Statistics.

Select the checkbox for Summary Statistics

Click OK.

Distribution Shape

is measured by skewness.

If the shape of the data is skewed to the left, the skewness

is negative;

if to the right then skewness is positive;

and if the data is symmetric, then skewness is zero.

For a symmetric distribution, the mean and median

are equal.

For a positively skewed distribution, the

mean is usually greater than the median and a

negatively skewed distribution, the mean is usually

less than the median.

How would we calculate skewness in excel?

=SKEW

Z scores

The z-Score yields a standardized value and is the

number of standard deviations from the mean.

The z-Score for any observation is a measure of the

relative location of the observation in the dataset.

Measures the relative location of values in the

dataset. This helps determine how far a particular

value is from the mean. z-Scores use the mean and

standard deviation in its calculation.

Chebyshev's Theorem

Allows us to make statements about the population

of the data values that must be within a specified

number of standard deviations from the mean.

At least (1 −1/ 𝑧^2) of the data values must be within

z standard deviations of the mean (z > 1).

It applies to any dataset.

If the data is bell shaped around the mean, we know

Approx. 68% of the data is within one s of ̅ 𝑥.

Approx. 95% of the data is within two s of ̅ 𝑥.

Approx. 99.7% of the data is within three s of ̅ 𝑥.

Outliers

are extreme values relative to the rest of

the data. z-Score can help identify outliers.

Typically, any z-Score greater than 3 is an

outlier.

Alternatively, we can use the interquartile range,

where the:

lower limit: 𝑄1 − 1.5(𝐼𝑄R)

upper limit: 𝑄3 + 1.5(𝐼Qr)

Covariance

is a descriptive measure of the linear

association between two variables.

If Covariance or s sub-xy> 0, then there is a positive linear association between x and y. If sxy < 0, then there is a negative linear association between x and y.

Be careful about attributing the size of the covariance and the strength of the linear relationship because covariance depends on the units of measurement.

correlation coefficient

The sample correlation coefficient ranges from -1 to

+1. If it is exactly 1 (perfect positive linear

relationship), then all the data would be on a

positively sloped line; and if it is exactly -1 (perfect

negative linear relationship), then all the data would

be on a negatively sloped line.

As the data deviates from the slope of the line, the correlation coefficient moves closer to zero.

How would we calculate covariance of a sample in excel?

=covariance.s

How would we calculate the Correlation Coefficient in excel?

=correl(

Probability

A numerical measure of the likelihood of an event

occurring. A probability ranges from 0 to 1, such as

the probability it will rain tomorrow.

experiment

Is a process generating well-defined outcomes.

Rolling a 6-sided die results in six possible outcomes:

S = {1, 2, 3, 4, 5, 6}

Counting rules for experiments

If an experiment has k steps with n1 possible

outcomes on step 1, n 2 possible outcomes on step 2,

and so on, then the total number of experimental

outcomes is (n1 )(n2 )...(nk ).

Thus, tossing a coin 6 times yields: (2)(2)(2)(2)(2)(2) =

64.

Permutations

a counting rule computing the number of

experimental outcomes when n objects are to be

selected from a set of N objects where the order of

selections is important.

Assigning Probabilities requirements

1. The probability assigned to each experimental

outcome must be between 0 and 1, inclusively

2. The sum of the probabilities for all experimental outcomes must be equal to 1.

Three methods to assign probability:

1. Classical Method - such as a coin toss or a roll of a

6-sided die.

2. Relative Frequency Method: is used when data are

available to estimate the proportion of time the experimental outcome will occur if the experiment is

repeated a large number of times.

3. Subjective Method: is used when outcomes are not

equally likely and data is unavailable.

Events

are a collection of sample points.

Example: Project Completion in 10 months or less:

C = {(2,6);(2,7);(2,8);(3,6);(3,7);(4,6)}

Probability of an event

The probability of an event is equal to the sum of the

probabilities of the sample points in the event. Thus,

P(C) = P(2,6)+P(2,7)+P(2,8)+P(3,6)+P(3,7)+P(4,6)

P(C) = 0.15 + 0.15 + 0.05 + 0.10 + 0.20 + 0.05 = 0.70

Complement of Event

are all the sample points not in the event.

Union of Two Events

the event containing all sample points belonging to Event A, Event B, or both.

The union of Event A and Event B is denoted by:

𝐴 ∪ 𝐵.

Intersection of Two Events

is the event containing the

sample points belonging to only both A and B.

The intersection is denoted by: 𝐴∩𝐵.

Addition Law

is useful when we want to know the

probability that at least one of two events occurs.

𝑃(𝐴 ∪ 𝐵) = 𝑃(𝐴) + 𝑃(𝐵) − 𝑃(𝐴 ∩ 𝐵).

Mutually Exclusive Events

occur when two events

have no sample

points in common.

Addition Law for

mutually exclusive

events:

𝑃(𝐴 ∪ 𝐵) = P (A) + P(B)

Conditional Probability

Often the probability of an event is influenced by

whether a related event already occurred. Suppose

Event A occurs with P(A). If Event B already occurred,

this new information results in a new probability for

Event A, and is called a conditional probability:

P(A|B)

Joint Probability

The probability of the intersection of two events.

Marginal Probabilities

is the sum of the joint probabilities (by row and

column).

Conditional Probability equations

𝑃(𝐴I𝐵) = 𝑃(𝐴 ∩ 𝐵)/𝑃(𝐵) or

𝑃(𝐵I𝐴) = 𝑃(𝐴 ∩ 𝐵)/𝑃(𝐴)

Independent Events

Event A and Event B are independent if:

P(A|B) = P(A) or P(B|A) =P(B)