Quantitative Business Analysis - Exam 1

Where is the box plot when the distribution is skewed?

To the left when the data is skewed right To the right when the data is skewed left

True or False: Box plots can also be vertical.

True

True or False: Nominal and Ordinal mean and measure the same as in Qualitative data.

True

What does the outer fence represent?

anything outside of the outer fence is considered an extreme outlier

What is ordinal data?

categories that have an implied ordering; order matters

What is crosstabulation?

compares 2 qualitative variables

What does an XY scatterplot do?

compares 2 quantitative variables

What is descriptive statistics?

creating tables, charts, and numerical summaries in an attempt to condense a large amount of information

What is Qualitative data?

data that records an attribute or category (labels)

What is nominal data?

distinct categories; can switch order and have no implication on the data

What 2 properties does a box plot show?

distribution and outliers

What is a population?

entire set of individuals or objects of interest

What is discrete data?

finite set of values with gaps in between; counting something

What does the Empirical Rule state?

for a symmetrical, bell-shaped distribution, approximately 68% of the observations will lie within 1 standard deviation from the mean (x̄ +/- 1s), 95% of the observations will lie within 2 standard deviations from the mean (x̄ +/- 2s), 99.7% of the observations will lie within 3 standard deviations from the mean (x̄ +/- 3s)

How do the scales of measurement measure?

from least sophisticated to most sophisticated

What is an interval?

greater than and less than relationships as well as units of measurement

What is a Ratio?

greater than and less than relationships, units of measurement, and absolute zero point

What are the units for the variance?

in squared units of measure

What is a shortcoming of the range?

its a weak measure as it is affected by outliers due to the fact that it only looks at outliers

What is the notation for the range?

max - min = Range

What is the definition of the standard deviation?

measures the "typical" dispersion of a set of data around its mean

What main points are shown on a box plot?

min, Q1, median, Q3, max

what is the symbol for the sample mean?

x̄ "x-bar"

What is the notation for sample mean?

x̄ = Σ (xi) / n or X1+X2...+Xn/n

What is the notation of the weighted mean?

x̄ w = Σ(wx)/Σw

What is the symbol for the population mean?

μ "mu"

What is the notation for the population mean?

μ = Σ (xi) / N or X1+X2...+XN/N

What is the notation for the population standard deviation?

σ = √Σ(Xi - μ)² / N

What is the symbol for population variance?

σ2

What is the notation for the population variance?

σ² = Σ(Xi - μ)² / N

How do you find the median in a data set?

1. Arrange/order the data 2. Position: (n+1)/2

What is a property of a ratio?

1. Multiples are meaningful

What are the properties of an interval?

1. Units of measure are random 2. has no absolute zero level when none is a quality present, thus multiples are not meaingful

What are the properties of the mean?

1. all values contribute equally 2. the most commonly used measure of central location 3. all values are used in its calculation 4. Mean: a balance point for a set of data 5. mean is affected by extreme values (skewed distributions) 6. Σ(Xi - x̄ ) = 0

What are the properties of a weighted mean?

1. not all values are of the same contribution 2. useful if data is presented in a frequency table

What are the properties of the median?

1. not all values are used in the calculation 2. not affected by outliers/skewed distribution

What are the 2 types of statistics?

Descriptive and inferential

What are the 2 types of quantitative data?

Discrete and Continuous

What does the table that compares the Empirical Rule to Chebyshev's Theorem look like?

Interval Empirical Rule Chebyshev's Theorem x̄ +/- 1s ~ 68% N/A x̄ +/- 2s ~ 95% _> 3/4 or 75% x̄ +/- 3s ~ 99.7% _> 8/9 or 89%

What is special about the mode?

Its the only numerical summary that is useful for qualitative data

What is the relationship between the mode, median, and mean in a skewed left distribution?

Mean < Median < Mode

What are the measures of central location?

Mean, Weighted Mean, Median, Mode

What is the relationship between the mode, median, and mean in a skewed right distribution?

Mode < Median < Mean

What are the 2 types of Qualitative Data?

Nominal and Ordinal

What are the scales of measurement?

Nominal, Ordinal, Interval, and Ratio

What is the first quartile?

Q1 = 25% of the data is less than or equal to Q1

What is the notation for the Interquartile Range?

Q3 - Q1 = IQR

What is the third quartile?

Q3 = 75% of the data is less than or equal to Q3

What are the 2 types of data?

Qualitative and Quantitative

What are the measures of dispersion?

Range, variance, standard deviation

What is the relationship when X decreases and Y decreases?

They have a negative correlation

What is the relationship when X increases and Y increases?

They have a positive correlation

What is the relationship when X and Y are random?

They have no correlation

What is the notation to find the inner fence?

[Q1 - 1.5(IQR)], [Q3 + 1.5(IQR)]

What is the notation to find the outer fence?

[Q1 - 3(IQR)], [Q3 + 3(IQR)]

What does the inner fence represent?

anything outside of the inner fence is considered a moderate outlier

What is a parameter?

numerical measure of a population

What is a statistic?

numerical measure of a sample

What is the definition of a percentile?

percent of the data less than or equal to a value

What is a sample?

portion of the population

What is inferential statistics?

procedures that involve using sample data to draw conclusions about a larger population

What does the variance do?

reflects the dispersion of all the values around the mean of the data; average of the squared deviations

What is Quantitive data?

results from a count or measure (numerical data)

What is the notation for the sample standard deviation?

s= √Σ(Xi - x̄ )² / (n-1)

What is the symbol for sample variance?

s²

What is the notation for the sample variance?

s²= Σ(Xi - x̄ )² / (n-1)

Where is the box plot when the distribution is symmetrical?

the center of the diagram

What is sampling error?

the difference between a parameter and statistic

What is the definition of the median?

the midpoint or center of a set of data

What does Chebyshev's Theorem state?

the proportion of observations in any sample that lie within K standard deviations of the mean is at least (1 - 1/K²) for K>1

What is the Interquartile Range?

the range of the "middle 50%" of the data

What units of measure does the standard deviation use?

the same, original units as the data

What is the definition of statistics?

the science of collecting, organizing, presenting, analyzing, and interpreting data to assist in making more effective decisions; tools to help understand information

What is the definition of the mode?

the value(s) that occur most frequently

What is continuous data?

theoretically infinite number of possible values (decimals); typically measuring something

What is the relationship between the mode, median, and mean in a symmetrical distribution?

they are all equal