Business Statistics Ch. 3

Front 1

Central tendency

Back 1

a single value used to describe the center point of a data set

Front 2

Measures of central tendency

Back 2

mean, median, and mode

Front 3

Mean

Back 3

AKA average, is the most common measure of central tendency;
add all values in a data set and divide the result by the number of observations

Front 4

Back 4

x- bar = sample mean
xi = the values in the sample
n = the number of data values in the sample

Front 5

Back 5

Mu - the population mean
N - the number of data values in the population

Front 6

Weighted mean

Back 6

allows you to assign more weight to certain values and less weight to others

Front 7

Back 7

wi - the weight for each data value xi
bottom of formula - the sum of all the weights

Front 8

Advantages of using mean to summarize data

Back 8

simple to calculate
summarizes the data with a single value

Front 9

disadvantages of using the mean to summarize data

Back 9

with only a summary value you lose information about the original data;
the value of the mean is sensitive to outliers

Front 10

median

Back 10

the value in the data set for which half the observations are lower and half are higher;
NOT sensitive to outliers

Front 11

formula for the index point for the median

Back 11

i = .5(n)
whenever the index point isn't a whole number, round the value up to the next highest whole number

Front 12

mode

Back 12

value that appears most often in a data set;
if no data value or category repeats, we say the mode doesn't exist;
more than one mode can exist if 2 or more values tie for most frequent;
particularly useful way to describe categorical data

Front 13

Which measure of central tendency should you use?

Back 13

mean is generally used, unless extreme outliers exist;
if outliers are present, the median is often used, since the median isn't sensitive to outliers;
for categorical data, the mode is the best choice

Front 14

Measures of variability

Back 14

show how much spread is present in the data;
range, variance, and standard deviation

Front 15

range

Back 15

simplest measure of variation;
difference between the highest value and the lowest value in a data set

Front 16

s^2 =

Back 16

sample variance

Front 17

Sample variance formula

Back 17

(xi - xbar) = the difference between each data value and the sample mean

Front 18

Standard deviation

Back 18

the square root of the variance;
has the same units at the original data

Front 19

Sample standard deviation formula

Back 19

Front 20

Population variance formula

Back 20

Front 21

coefficient of variation (CV)

Back 21

measures the standard deviation in terms of its percentage of the mean;
a high cv indicates high variability relative to the size of the mean and vice-versa;
a smaller coefficient of variation indicates more consistency within a set of data values

Front 22

sample coefficient of variation formula

Back 22

Front 23

population coefficient of variation formula

Back 23

Front 24

z-score

Back 24

identifies the number of standard deviations a particular value is from the mean of its distribution;
has no units;
0 for values equal to the mean;
positive for values above the mean;
negative for values below the mean;

Front 25

z-score of an outlier

Back 25

is above +3 or below -3

Front 26

population z-score formula

Back 26

Front 27

sample z-score formula

Back 27

Front 28

The empirical rule

Back 28

if a distribution follows a bell-shaped, symmetrical curve centered around the mean, we would expect:
approx 68% of the values to fall within +/- 1 standard deviations from the mean;
approx 95% of the values to fall within +/- 2 standard deviations from the mean
approx 99.7% of the values to fall within +/- 3 standard deviations from the mean

Front 29

population z-score in terms of x formula

Back 29

Front 30

sample z-score in terms of x formula

Back 30

Front 31

Measures of relative position

Back 31

Measures of relative position compare the position of one value in relation to other values in the data set;
Percentiles and quartiles

Front 32

Percentiles

Back 32

measure the approx percentage of values in the data set that are below the value of interest

Front 33

find percentiles manually

Back 33

sort the data from lowest to highest;
calculate the index point, i;
if i is not a whole number, round it to the next whole number;
if i is a whole number, the midpoint between i and i+1 position is our value

Front 34

percentile rank

Back 34

identifies the percentile of a particular value within a set of data

Front 35

percentile rank formula

Back 35

Front 36

quartiles

Back 36

split the ranked data into 4 equal groups:
the 1st quartile (Q1) constitutes the 25th percentile;
the 2nd quartile (Q2) constitutes the 50th percentile (also is the median);
the 3rd quartile (Q3) constitutes the 75th percentile

Front 37

Interquartile Range (IQR)

Back 37

describes the middle 50% of a range;
find the IQR by subtracting the first quartile from the third quartile;

Front 38

Box and whisker plot

Back 38

is a graphical display showing the relative position of the three quartiles as a box on a number line;
also shows the min and max values in the data set and any outliers