20-30 mins for canvas, 1 hr for excel
Will geometric and arithmetic mean rate of return be on the test? No
5 number summary? Yes
When do we use INC vs. EXE for QUART.
Will we need to calculate what is +/- 1 standard deviation of the mean? Yes
Types of Data & Intro to Spreadsheets
●​ Identify variable types in the context of a business problem.
Categorical: variables take categories as their values such as “yes”, “no” or “blue”, “brown”,
“green”, “order #”, “ID #”. Domain is a list of values.
➔​ Defined Categories: Marital status, eye color, supplier, item description, date as month;
Aug, Sept, etc
➔​ Ordered Categories: ratings, low, med, high, date as month and year; Aug 2021, order
size, emergency designation, AP term designation
Numerical (quantitative): variables have values that represent a counted or measured
quantity. Domain is a range.
➔​ Discrete Examples: How many text messages have you sent? Item #, quantity, future
orders made, AP Terms. Can be negative, a whole number, and is a counting process
➔​ Continuous Examples: How long did the mobile app take to download? Item cost, total
future cost, date down to second. Can be a decimal and is a measuring process
Overall: Categorical random variables yield categorical responses such as yes or no
answers. Numerical random variables yield numerical responses such as your height in
inches.
●​ Describe the difference between populations and samples, and parameters and
statistics.
Population: all the items or individuals you seek to study. Ex) everyone you want to sell your
product too
Sample: only a portion of a population of items or individuals
Population Parameter: summarizes the value of a specific variable for a population. Ex)
Population mean: u
Population Statistic: Summarizes the value of a specific variable for sample data. Ex) Sample
mean:
A statistic is a summary measure describing a sample whereas a parameter is a
summary measure describing an entire population.
●​ Understand differences in types of data and measurement scales.
Greek letters mean pop and normal means sample
Primary sources: data collector is the one using the data for analyse; experiment, observed
Secondary sources: person performing data analysis is not the data collector
Stacked data: single column for the variable of int. & create/add columns for the potential
grouping of variables
Unstacked data: separate numerical variables for diff groups
Measurement scales - whether differences matter
●​ Nominal: classifies data into distinct categories w/out ranking or order. Ex) type of
investment can be growth, value, other
●​ Ordinal: classifies data into distinct categories w/ ranking. Ex) Student class; freshman,
sophomore
●​ Interval: difference b/t measurements matter but have no zero point. Ex) date/time, SAT
score, temperature (c or f) → can be neg
●​ Ratio: ordered scale where diff b/t measurements is a meaningful quantity and the
measurements have a zero point. Ex) weight, distance, duration (length of time), salary,
age
●​ → needs a starting point such as the end of a semester
●​ Know how to use basic Excel commands to:
○​ Average: Calculate the mean of a dataset. For an average for a specific range
do =AVERAGEIF(range, criteria, [range you are average]).Ex)
Average female backpack weight = Sex range, “female”, backpack weight
➔​ Use AVERAGEIFS: Q: Average backpack weight for students who are
Male Business (Bus) Majors=AVERAGEIFS(average_range,
criteria_range1, criteria1, ...)
○​ Count: Determine the number of entries in a dataset. Look for “total”, “number”,
“proportion”. Ex) Number of students who have a backpack weight that is at least
10% of their body weight =COUNTIF(J2:J101(ratio), ">=.1")
➔​ Proportion of students who have a back problem =COUNTIF(D2:D101,
"Yes")/100
○​ Categorize: Group data based on specific attributes.
○​ Summarize: Extract key insights from data.
○​ Round: =ROUND(number, # of digits you want to round too)
Q: Designate a student as "Suspected backpack issue" if they have back problems and
their backpack is at least 10% of their bodyweight
A: =IF(AND(D2="Yes", J2>=0.1), "Suspected backpack issue", "")
Q: Designate a student as either: "Part Time" (Units<14), "Full Time" (Units =14), or
"Overload" (Units >14)
A: =IFS(I2<14, "Part Time", I2=14, "Full Time", I2>14, "Overload")
Visualizations (Including Histograms)
●​ Define, construct, and interpret histograms and boxplots.
Histogram: y axis is data range, x-axis is bins.
Cumulative Percentage: Dotted line chart, put frequency as y-axis and bins on x-axis
●​ Use scatter plots to articulate relationships between two numeric variables.
Scatter plots are used for numerical data consisting of paired observations taken from two
numeric variables. One variable’s values are displayed on the horizontal x-axis and the other’s
is displayed on the vertical y-axis. They examine possible relationships b/t two variables.
●​ Interpret the relationship between bar charts and their corresponding categorical
variables.
-​ For side-by-side bar charts, put the columns on the horizontal axis, rows on vertical.
-​ Best visualization for plotting relationship b/t two variables, where one is categorical and
one is numerical → column/bar chart or pie chart
●​ Be able to create any chart covered in class or homework.
●​ Identify the most appropriate visualization type given the variables in a business
context.
Numerical Descriptive Measures
●​ Define and compute measures of central tendency (mean, median, mode) and
interpret them in business problems.
Central tendency: extent that values of a numerical variable group around a typical/central
value.
●​ Mean: arithmetic mean is the most common measure of central tendency, affected by
extreme values (outliers), sum of values/# of values. Excel: =AVERAGE
●​ If mean > median it indicates right skewness
●​ If mean = median it indicates symmetry
●​ Median: “Middle number” 50% above, 50% below. Less sensitive than the mean to
extreme values. If the number of values is even, the median is the avg of the two middle
numbers. Example in problem: if you have a total # of observations, multiply it by 0.5 to
get the amount of facilities with a score lower than or equal to the median. = MEDIAN
●​ Mode: Value that occurs most often, not affected by extreme values, used for numerical
or categorical data, there may be no mode or several modes. =MODE.SNGL
Mean is generally used, unless extreme values (outliers) exist.
Median is often used since it is not sensitive to extreme values
Makes sense to report both median and mean.
●​ Define, compute, and differentiate measures of variation (range, variance, standard
deviation) in a business context.
Measures of variation: information on spread, variability or dispersion of the data or values.
●​ Range: max-min, does not account for how data is distributed and sensitive to outliers
●​ Variance: Average (approximately) of squared deviations from the mean
●​ Sample Standard Deviation: “average” deviation from the mean, shows variation about
the mean, is the square root of the variance, has the same units as the original data
The more data spread out, the greater the range, variance, and std dev, and if it's smaller its
more concentrated
If the values are all the same (no variation), all these measures are 0 and a measure cannot be
neg
●​ Define and compute percentiles and quartiles in Excel.
Percentile: Shows the relative standing (by the index of items when sorted. Kth
percentile is where most observations lie, n=total # of observations.
The Excel function PERCENTILE.INC(array, k) computes the kth percentile of data in
the range specified in the array field, where k is in the range 0 to 1, inclusive (i.e.,
including 0 and 1).​
Quartile: Break data into 4 parts.
●​ The 25th percentile is called the first quartile,Q1; ​
●​ The 50th percentile is called the second quartile, Q2; ​
●​ The 75th percentile is called the third quartile, Q3; and ​
●​ The 100th percentile is the fourth quartile, Q4. ​
Excel function QUARTILE. INC(array, quart), where array specifies the range of the data
and quart is a whole number between 1 and 4, designating the desired quartile.​
●​ Articulate the impact of outliers on measures of central tendency.
●​ To compute the Z-score of a data value, subtract the mean and divide by the
standard deviation.​
●​ Z-score is the number of standard deviations a data value is from the mean.​
●​ data value is considered an extreme outlier if its Z-score is less than -3.0 or
greater than +3.0.​
●​ Define symmetric, left-skewed, and right-skewed distributions.
Skewness: extent to which data values are not symmetrical
=SKEW(
For correlation value or Coefficient of correlation =CORREL
To find what's in the top 10% of “category”, take the output from the 90th Percentile and use
=COUNTIF(C12:C7473, ">192.843(90th percentile output)")
Linear Models in Business
●​ Construct and graph linear models using data points, slopes, and given business
contexts.
Supply and Demand (Line chart): Supply and demand on y axis, price goes on x-axis without
labels by selecting data
Breakeven (Line chart): Revenue, total cost and profit on y-axis, quantity on x-axis without
labels by selecting data.
●​ Construct linear cost, revenue, profit, supply, and demand models in a business
setting.
Linear cost: Total money spent creating the item
= (fixed cost)+(cost per unit) * quantity of units sold = F + V * Q
Revenue: Money earned from selling the item
= (price of a unit) * (quantity of units sold)= P * Q
Profit: Total Revenue - Total Cost
= PQ - (F+VQ)
Supply and Demand: Price is determined by the relationship b/t supply & demand
The price tends to stabilize when at the point of intersection of the demand & supply equations.
Supply is positive, find (price, supply), do y2 - y1/x2-x1 and find y-intercept
Demand is negative, find (price,demand), do y2 - y1/x2-x1 and find y-intercept
Both slope equations use x as the price to solve for demand and supply at different prices.
●​ Calculate intersections of linear models and interpret break-even points and
equilibrium prices.
Supply and demand: equilibrium point is when supply and demand intersect, when Qs=Qd
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Point of intersection is called the equilibrium point
Corresponding price is called the equilibrium price
-​
Equilibrium quantity is when Q=S=D
Break Even Point: Break Even point is when a business stops losing money and starts gaining
money. When TC=TR.
A breakeven analysis is used to determine the amount of production/sales required for a
business to “break even”.
Basic Probability Concepts
●​ Identify events, sample space, unions, intersections, and complements.
Sample space: collection of all possible outcomes of a variable. Ex) all 6 faces of a die, all 52
cards of a card deck
Events:
➔​ Simple event: Event described by a single characteristic. Ex) Drawing just an ace
➔​ Joint event: An event described by 2 or more characteristics. Ex) Drawing an Ace of
Diamonds
➔​ Complement of and Event A (denoted A’): All events that are NOT part of event A. Ex)
Drawing anything that's not an Ace
Probability is the numerical value representing the chance, likelihood or possibility that an
event will occur
Impossible Event: zero probability of
occurring. Ex) cannot pull a card w a negative
#
Certain Event: 100% chance of occurring
Ex) Pulling a card that isn’t blank
Mutually exclusive Events: Events cannot
occur simultaneously. Ex) Cannot pull a king
and queen
Collectively Exhaustive Events: One event
MUST occur and the set of events covers the
entire space. Ex)
●​ Identify applications of simple, compound, and conditional probability in business
contexts. Along with independence
Add joint probabilities
If A and B are mutually
exclusive, then P(A + B)=0, so the rule is simplified
-​
Joint probabilities show the overlap and you can remove the overlap by
subtracting by the joint probability using the General Addition Rule.
=Joint/Marginal
Independence:
●​ Events A and B are independent when the event of B taking place doesn’t affect A.
Independent if P(A|B)=P(A)
●​ Different #’s in events mean they’re not independent
●​ Probability of one event is not affected by the fact that the other event occurred.
-​ Compare simple to joints
●​ Compute probabilities using:
○​ 2-way contingency tables.
○​ Excel pivot tables for large datasets.
○​ Expected value and variance from sample statistics.
Normal Continuous Distribution
●​ Define continuous normal distributions, including expected value and variance.
Is a continuous variable and standardized normal distribution the same?
Key features, value and variance:
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mean=median=mode
IQR/Std dev = 1.33
Range/std dev = 6
bell-shaped → kurtosis=0
symmetrical→ skew=0
mean controls center location(distribution left or right)
std dev controls the width(increases or decreases the spread
x represents all outcomes (sample space)
Examples of what fits normal distribution: test scores, height, weight, production error,
age you stop school
●​ Calculate the area under a probability density function and understand its
significance.
Lower-tail probability: P(x<15) =NORM.DIST
Upper-tail probability:P( x>25) = 1 - NORM.DIST
Probability b/t two values: P(16<x<20) = P(x<20) - P(x<16) = NORM. DIST (x larger, mean,
st dev, TRUE) - NORM.DIST (X smaller, mean, st dev, TRUE)
Finding the x-value or z-value for a given probability: How long does it take for 90% of the
images to be downloaded?x =NORM.INV, for z-value use z= NORM.S.INV (probability)
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For “top”, “more than, “heaviest” → What amt of time do the top 10% of teachers
work? =NORM.INV(0.9, 20, 5)
●​ Determine and interpret the desired area under a probability density function in
relation to business problems, including probability thresholds and variable thresholds.
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-​ Variable is how it relates to the question; interpreting the result of a percent
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●​ Compute and interpret z-scores for standardization.
Z distribution always has a mean = 0 and standard dev = 1. Excel: =STANDARDIZED
●​ Test 1 format: Questions will be of the form: hw 3-8
○​ P(X<x)P(X < x)P(X<x)
○​ P(X>x)P(X > x)P(X>x)
○​ P(x1<X<x2)P(x_1 < X < x_2)P(x1​<X<x2​)