Statistics

Question 1

three methods of graphing grouped quantitative data

Answer 1

1. Histogram - classes are marked on the horizontal axis, frequencies/relative frequencies/percentages on the y
2. polygon - graph formed by joining the midpoints of the tops of successive bars in a histogram with straight lines
3. frequency distribution curve - where the frequency polygon eventually becomes a smooth curve

Question 2

shapes of histograms

Answer 2

symmetric
skewed
uniform/rectangular

Question 3

Skewed right

Answer 3

tail is longer on the right side

mean will be greater than median

Question 4

skewed left

Answer 4

tail is longer on the left side

mean will be less than the median

Question 5

cumulative relative frequency

Answer 5

cumulative frequency / total observations in the dataset

Question 6

stem and leaf for the number 46

Answer 6

4|6

Question 7

5|2 which is the stem and which is the leaf

Answer 7

stem is 5
leaf is 2

Question 8

major shortcoming of the mean as a measure of central tendency is that

Answer 8

it is very sensitive to outliers

Question 9

median

Answer 9

value of the middle term of the data set ranked in increasing order

it is not influenced by outliers

Question 10

mode will be greater than / less than mean for a left skew

Answer 10

mode will be greater than the median and the mean

Question 11

order for mean, median, mode for left skew

Answer 11

mean, median, mode

Question 12

order of mean, median mode for right skew

Answer 12

mode, median, mean

Question 13

variance

Answer 13

for a population = σ2

for a sample = s2

calculated as: the sum of all your (values - the mean)squared / sample size

Question 14

standard deviation

Answer 14

positive square root of the variance

provides a measure of dispersion of ABSOLUTE variability, not of relative variability

Question 15

when we want to compare variablity of two different data sets, we have to use

Answer 15

the coefficient of variation

Question 16

coefficient of variation

Answer 16

expresses the standard deviation as a percentage of the mean

CV = (the standard deviation / the mean) x 100%

Question 17

mean of a population/sample is calculated as

Answer 17

the sum of the midpoint multiplied by the frequency divided by the population number/sample number

Question 18

Chebyshev’s theorem for standard deviation

Answer 18

for any number (k) greater than 1, at least ( 1 - 1/k^2 ) of the data values lie within k standard deviations of the mean. K can be 1 but it cannot be less than 1.

Question 19

Empirical rule for Chebyshev’s theorem

Answer 19

68% of the observations lie within one std dev of the mean

95% of the obvs lie within 2 std dev of the mean

99.7% of the obvs lie within 3 std dev of the mean

Question 20

quartiles

Answer 20

three summary measures (Q1 Q2 Q3) that divide a ranked data set into four equal parts

Question 21

first quartile definition

Answer 21

the midpoint between the median and the minimum

Question 22

third quartile

Answer 22

the midpoint between the median and max

Question 23

how do you find the median

Answer 23

rank all data points in order, pick the middle one

location of Q2/median = (n + 1)/2

if there is an even number of data points, you add up the two values on either side of the mean location and divide it by two (see example on page 6 of 5.3)

Question 24

percentile definition

Answer 24

the summary measures that divide a ranked data set into 100 equal parts. each data set has 99 percentiles.

the Kth percentile = a value in a data set such that about K% of the measurements are smaller than the value of Pk and about (100-k)% of the measurements are greater than the value of Pk

Question 25

how to find the location of a percentile

Answer 25

K(n)/100 ex: find Pk for the 42 percentile Kn/100 = (42 x 12)/100 = 5.04 locate the value of the 5th term in your ranked data set. If it was 5.9, you would pick the 6th term (suppose it is 11 billion) you would then say "approximately 42% of _____ had ______ less than or equal to 11 billion

Question 26

finding percentile rank of x ex: find the percentile rank for x what does this tell you

Answer 26

percentile rank = [(number of values less than x) / (total number of values in the data set)] x 100% lets say you found the percentile rank to be 67% - this means that about 67% of the companies had a ____ less than x helps you determine what percentile some value is

Question 27

equation of the lower inner fence

Answer 27

Q1 - 1.5(IQR)

Question 28

equation of the upper inner fence

Answer 28

Q3 + 1.5(IQR)

Question 29

Left skewed box plot

Answer 29

distance between minimum to the median is larger than distance between median to maximum

Question 30

relative frequency

Answer 30

if an experiment is completed n times, and an event A is observed f times then probability (according to relative frequency concept) is: P(A) = f/n

Question 31

law of large numbers (probability and relative frequency)

Answer 31

if you repeat an experiment multiple times, the probability of an event obtained from relative frequency approaches the actual or theoretical probability

Question 32

subjective probability

Answer 32

the probability assigned to an event based on subjective judgement, experience, and belief

Question 33

determining total outcomes when you have an experiment with multiple steps

Answer 33

multiple the number of outcomes for each of the steps

Question 34

marginal probability (simple probability)

Answer 34

the probability of a single event without the consideration of any other event

Question 35

probability

Answer 35

a numerical measure of the likelihood that a specific event will occur denoted by P probability lies between 0 and 1

Question 36

symbol for the probability of a simple event (Ei)

Answer 36

P(Ei)

Question 37

conditional probability

Answer 37

the probability that an event wil occur given that another event has already occurred P(A\B) = the probability of A given that B has already occurred

Question 38

independent events

Answer 38

when the occurence of one does not affect the probability of the occurrence of the other

Question 39

complementary events

Answer 39

the complement of event A is denoted by A(line on top) and is described as the event that includes all the outcomes for an experiment that are not in A

Question 40

intersection of events

Answer 40

the collection of all outcomes that are common to both A and B

Question 41

joint probability

Answer 41

the probability of the intersection of two events P(A and B) P(A and B) = P(A) P(B|A)

Question 42

union of events

Answer 42

all outcomes of either event a or b P(A or B) = P(A) + P(B) - P(A and B)

Question 43

probability distrubution (discrete random variable)

Answer 43

lists all the possible values the random variable can assume and their corresponding probabilities

Question 44

the mean of a discrete random variable

Answer 44

x - also called the expected value, and is denoted by E(x)