OMIS 1050 WEEK 4

What are descriptive statistics?

stat technique & number measure foundation

What are descriptive statistics’ use?

initial data understanding in business analytics to understand meaning / relationship

What are the centre & location measures?

• mean

• median

• mode

• weighted mean

• geometric mean

What are the rank measures?

• percentile

• quartile

• box plot

What are the variation measures?

• range

• mean absolute deviation

• variance

• standard deviation

• coefficient of variation

• covariance

• coefficient of correlation

What denotes paramaters?

• Greek letter

What denotes statistics?

• Roman letter

• Greek letter with carat

What denotes a population mean?

μ

What denotes a sample mean?

x̄

Do outliers affect the mean?

yes

Do outliers affect the median?

slightly

What is the mode’s main use?

nominal data

Do outliers affect the mode?

no

What denotes a weighted mean?

x̄_w

What is the weighted mean formula?

(sum of values * weights) / sum of weights

What does the mean describe?

interval data central location

What does the median describe?

interval / ordinal data central location

What does the mode describe?

nominal data

What does the geometric mean describe?

growth rate interval data

What is the mean & median & mode relationship in a symmetrical distribution?

all =

What is the mean & median & mode relationship in a distribution skewed right?

mode < median < mean

What is a skewed right synonym?

positively skewed

What is the mean & median & mode relationship in a distribution skewed left?

mean < median < mode

What is a skewed left synonym?

negatively skewed

What does a positively skewed distribution look like?

What does a negatively skewed distribution look like?

What’s an advantage of the range?

compute ease

What’s a disadvantage of the range?

dispersion info absence

What is the deviation?

value & mean difference

What is the deviation formula?

value - mean

What is the average deviation value?

0

What does MAD stand for?

Mean Absolute Deviation

What’s the MAD’s use?

forecast model

What is the MAD formula?

(sum of absolute deviations) / item number

What are the most important descriptive statistics?

• variance

• standard deviation

What denotes population variance?

σ²

What denotes sample variance?

s²

What is the variance calculation numerator?

sum of squared deviation

What is the population variance formula?

sum of squared deviation / population size

What is the sample variance formula?

sum of squared deviation / (sample size - 1)

What is the sample variance shortcut formula?

(sum of squared values - [square of summed values] / sample size) / (sample size - 1)

What denotes population standard deviation?

σ

What denotes sample standard deviation?

s

What is the standard deviation’s use?

• compare distribution variability

• make distribution shape statement

What is a relative position measure?

z-score

What is the z-score?

standard deviation number from mean

What is a z-score synonym?

standardized data

What is the z-score formula?

(value - mean) / standard deviation

What is the z-score Excel formula?

• =STANDARDIZE

What are the linear relationship measures?

• covariance

• coefficient of correlation

What is covariance?

2 variable pattern

What is coefficient of correlation?

2 variable pattern strength

What are rank measures’ use?

• compare value rank

What is a percentile?

value dividing data in 100 equal parts

What is a quartile?

value dividing data in 4 equal parts

What is the percentile position formula?

(item element + 1)(percentile / 100)

What denotes the percentile position?

L_P

What is the percentile formula if the position is not whole?

lower rounded value + percentile position * (upper rounded value - lower rounded value)

What is the percentile Excel formula?

• =PERCENTILE.EXC

What does IQR stand for?

InterQuartile Range

What is the IQR?

3rd & 1st quartile differenceWh

What is the IQR formula?

Q₃ - Q₁

What is the IQR’s use?

middle 50% range

What is a box plot synonym?

box & whisker plot

What does the box plot show?

Q₁, Q₂, Q₃ using box & range using whisker

What is the max whisker length past the box?

1.5 * IQR

How do you plot outliers beyond the whisker?

individual point

When can you use the empirical rule?

normal distribution

What’s the empirical rule’s use?

approximate value percent within standard deviation number

What total percent of items fall within 1 standard deviation?

34% + 34% = 68%

What percent of items fall within 2 standard deviations?

13.5% + 13.5% = 27%

What total percent of items fall within 2 standard deviations?

68% + 27% = 95%

What percent of items fall within 3 standard deviations?

2.35% + 2.35% = 4.7%

What total percent of items fall within 3 standard deviations?

95% + 4.7% = 99.7%

What is the coefficient of variation’s use?

• express standard deviation relative to mean with different data means

What is a coefficient of variation application?

finance

• risk to return

What is said about larger coefficients of variation?

greater relative spread

What is the coefficient of variation formula?

standard deviation / mean * 100%

What is the population covariance formula?

sum of deviation products / population size

What is the sample covariance formula?

sum of deviation products / (sample size - 1)

What is the sample covariance shortcut formula?

(1 / sample size - 1)(sum of variable products - [sum of variable 1 * sum of variable 2 / sample size)

What will the covariance value be if 2 variables move the same direction?

large + value

What will the covariance value be if 2 variables move the opposite direction?

large - value

What will the covariance value be if there is no 2 variable pattern?

value close to 0

What is the coefficient of correlation formula?

covariance / (standard deviation 1 * standard deviation 2)

What denotes the population coefficient of correlation?

p

What is the coefficient of correlation range?

-1 - 1

What will the coefficient of correlation value be if the 2 values have a strong positive linear relationship?

value close to 1

What will the coefficient of correlation value be if the 2 values have a strong negative linear relationship?

value close to -1

What will the coefficient of correlation value be if the 2 values have no straight linear relationship?

value close to 0

What is the coefficient of correlation Excel formula?

• =CORREL

• Data → Data Analysis → Correlation

What is the sample covariance Excel formula?

• =COVARIANCE.S

What is the population covariance Excel formula?

• Data → Data Analysis → Covariance

What table should you create when calculating the covariance, variance, standard deviation, and coefficient of correlation?

sum of & X	sum of & Y	sum of & X*Y	sum of & X2	sum of & Y2
* covariance * variance	* covariance * variance	* covariance	* variance	* variance

What are the geometric mean’s uses?

• multiplicative values

• wide range

• compare changes over time

What is the geometric mean formula?

(product of 1 + growth rate)^1/size - 1

What function returns the cell number matching criteria?

• =COUNTIF

What function sums numbers?

• =SUM

• Home → Σ

What function returns the population variance?

• =VAR.P

What function returns the sample variance?

• VAR.S

• Data → Data Analytics → Descriptive Statics → toggle “Summary statistics”