Chptr 3 & 4 Study Guide

Question 1

Mean

Answer 1

(μ, x̄) sum of data values / # of values; x̄ = ( Σx ) / n

Question 2

Mode

Answer 2

value(s) w/ greatest occurring frequency; qualitative and quantitative; doesn’t get rounded; possible for no modes or more than one modes

Question 3

Median

Answer 3

middle value when original data values are in increasing / decreasing order; resistant & doesn’t directly use every data value; find mean of two medians when even number set

Question 4

Midrange

Answer 4

Max value + min value /2; not resistant

Question 5

Range

Answer 5

max value - min value; non-resistant; doesn’t use all data sets

Question 6

Variance

Answer 6

set of values is a measure of variation equal to the square of the standard deviation; nonresistant, squares of the units of the original data values, never negative, unbiased estimator
• Sample s^2= square of the standard deviation s.
• Population variance σ ^2= square of the population standard deviation

Question 7

Round-off Rule for Measures of Center

Answer 7

mean, median, and midrange = carry one more decimal place than is present in the original set of values.
mode = leave the value as is without rounding

Question 8

Standard deviation

Answer 8

(s) a measure of how much data values deviate away from the mean ; never negative, larger values = more variation, nonresistant, same units as original data, biased estimator
- s sample = √Σ (x - μ)^2 / n - 1
- σ (population) = √Σ (x - μ)^2 / N)

Question 9

Locate mode, median, and mean in bell-shaped, positive, and negative-skewed distribution

Answer 9

normal: mean, median, mode are all in the center
positively skewed: mean = center; median = btwn mode + mean; mode = far left (top of slope)

Question 10

Resistant

Answer 10

presence of extreme values (outliers) doesn’t cause it to change very much

Question 11

Resistant measures of center

Answer 11

median, mode

Question 12

Nonresistant measures of center

Answer 12

Mean, midrange, range, variance, standard deviation

Question 13

z score

Answer 13

(z) How many standards deviations away it is from the mean (round to two decimal places);
- sample: x - x̄/s
- population: x - x̄/σ

Question 14

When is the standard deviation of a data set zero if ever?

Answer 14

when all values are exactly the same

Question 15

weighted mean

Answer 15

x̄ = Σ(wx)/Σw

Question 16

When to use a weighted mean

Answer 16

When different r data values are assigned

Question 17

Range Rule of Thumb

Answer 17

If I got 2 standard deviations up or down from the mean, it represents 95% of the sample values; applies to all shapes
- Significantly low values: μ - 2σ or lower.
- Significantly high values: μ + 2σ or higher.
- Values not significant: Between (μ - 2σ) and (μ + 2σ)

Question 18

Empirical Rule

Answer 18

for data sets having a distribution that is approximately bell-
shaped, (mean + or - (1,2,3,)SD)
- About 68% of all values fall within 1 standard deviation of the mean.
- About 95% of all values fall within 2 standard deviations of the mean.
- About 99.7% of all values fall within 3 standard deviations of the mean.

Question 19

Coefficient of Variation

Answer 19

(CV) for a set of nonnegative sample or population data, expressed as a percent, describes the standard deviation relative to the mean;
- sample: s/x̄ (100)
- population: σ/x̄ (100)

Question 20

First Quartile

Answer 20

(Q1, P25) It separates the bottom 25% of the sorted values from the top 75%.

Question 21

Second Quartile

Answer 21

(Q2, P50) same as the median; it separates the bot-
tom 50% of the sorted values

Question 22

Third Quartile

Answer 22

(Q3, P75) it separates the bottom 75% of the sorted
values from the top 25%.

Question 23

Interquartile Range

Answer 23

(IQR) = Q3 - Q1

Question 24

5-number summary

Answer 24

1. Minimum
2. Q1
3. Q2
4. Q3
5. Maximum

Question 25

Percentile

Answer 25

kth percentile being used

Question 26

In a modified boxplot, a data value is an outlier if it is

Answer 26

- above Q3, by an amount greater than 1.5 X IQR - below Q1, by an amount greater than 1.5 X IQR

Question 27

Boxplot

Answer 27

Box like graph that consists of the 5- number summary

Question 28

Probability

Answer 28

# btwn 0 & 1; 1 = certain to happen; ->1 = more likely to happen ->0 = less likely 0 = no chance

Question 29

event

Answer 29

any collection of results or outcomes of a procedure.

Question 30

simple event

Answer 30

outcome or an event that cannot be turther broken down into simpler components (one instance only)

Question 31

Sample space

Answer 31

procedure consists of all possible simple events. That is, the sample space consists of all outcomes that cannot be broken down any further; HHH, HHT, HTT, TTT

Question 32

Law of Large Numbers

Answer 32

“As procedure is repeated again and again, relative frequency probability of an event tends to approach the actual probability.”

Question 33

Compliment

Answer 33

All outcomes in which event A does NOT occur

Question 34

Relative Frequency Approx of Probability

Answer 34

P(A) = # of times A occurred / # time experiment repeated

Question 35

Classical Probability

Answer 35

P(A) = # of ways A occurred / # of different simple events

Question 36

biased estimator

Answer 36

they do not target the value of the corresponding population parameter; (Median, Range, Standard deviation )

Question 37

unbiased estimator

Answer 37

they each target the value of the corresponding population parameter (with a sampling distribution having a mean equal to the population parameter): (Proportion, Mean, Variance)

Question 38

Subjective Probability

Answer 38

P(A) estimated by using knowledge of relevant circumstances

Question 39

Range Rule of Thumb for Standard Deviation

Answer 39

s = range/4

Question 40

Outcome

Answer 40

specific event (HTH, HHT, etc.)