Chapter 2 - Describing Data with Numerical Measures

Question 1

Graphical methods may not always be sufficient for describing data. __ __ can be created for both populations and samples

Answer 1

numberical measures

Question 2

a numerical descriptive measure calculated for a population. Fixed (unknown) value.

Answer 2

Parameter

Question 3

a numerical descriptive measure calculated for a sample. Varies over samples

Answer 3

Statistic

Question 4

A measure along the horizontal axis of the data distribution that locates the center of the distribution.

Answer 4

Measure of Center

Question 5

the sum of the measurements divided by the total number of measurements.

Answer 5

MEAN

Question 6

Sample Mean

Answer 6

x-bar = Σ(xi) / n n = sample size (# of measurements)

Question 7

If we were able to enumerate the whole population, the population mean would be called?

Answer 7

µ (mew)

Question 8

the middle measurement when the measurements are ranked from smallest to largest

Answer 8

MEDIAN

Question 9

Position of the Median (equation)

Answer 9

.5(n +1)

Question 10

The measurement which occurs most frequently

Answer 10

Mode

Question 11

The __ is more easily affected by extremely large or small values than the __.

Answer 11

mean, median

Question 12

The __ is often used as a measure of center when the distribution is skewed

Answer 12

median

Question 13

Mean vs Median 1) Symmetric 2) Skewed right 3) Skewed left

Answer 13

1) Mean = Median 2) Mean > Median 3) Mean < Median

Question 14

A measure along the horizontal axis of the data distribution that describes the spread of the distribution from the center.

Answer 14

Measure of Variability

Question 15

Difference between the largest and smallest measurements.

Answer 15

Range (R)

Question 16

Measure of variability that uses all the measurements. Measures the average (squared) deviation of the measurements about their mean

Answer 16

Variance

Question 17

The variance of a POPULATION of __ measurements is the average of the squared deviations of the measurements about their mean __.

Answer 17

N, µ

Question 18

The variance of a SAMPLE of __ measurements is the sum of the squared deviations of the measurements about their mean, divided by ___.

Answer 18

(n-1)

Question 19

Variance of a Population (equation)

Answer 19

Question 20

Variance of a Sample (equation)

Answer 20

Question 21

1) In calculating the variance, we squared all of the deviations, and in doing so changed the __ of the ___.
2) To return this measure of variability to the original units of measure, we calculate the __ __.

Answer 21

1) Scale of the Measurements
2) Standard Deviation

Question 22

1) Standard Deviation of POPULATION
2) Standard Deviation of SAMPLE

Answer 22

Question 23

The value of s is ALWAYS ?

Answer 23

positive

Question 24

The larger the value of s2 or s, the larger the __ of the __ __.

Answer 24

variability of the data set.

Question 25

Calculational Formula for Sample Variance

Answer 25

Question 26

Definition Formula for Sample Variance

Answer 26

Question 27

Tchebysheff's Theorem

Answer 27

Given a number k ≥ 1 and a set of n measurements, at least 1-(1/k2) of the measurement will lie within k standard deviations of the mean.

Question 28

Tchebysheff’s Theorem 1) If k=2? 2) If k=3?

Answer 28

1) at least 3/4 of the measurements are within 2 standard deviations of the mean. 2) at least 8/9 of the measurements are within 3 standard deviations of the mean.

Question 29

Empirical Rule Given a distribution of measurements that is approximately mound-shaped: 1) The interval µ ± σ contains approximately \_\_% of the measurements. 2) The interval µ ± 2σ contains approximately \_\_% of the measurements. 3) The interval µ ± 3σ contains approximately \_\_% of the measurements.

Answer 29

a) 68% b) 95% c) 99.7%

Question 30

Tchebysheff's Theorem must be true for which data sets?

Answer 30

ALL

Question 31

1) From Tchebysheff’s Theorem and the Empirical Rule, we know that R ≈ ? 2) To approximate the standard deviation of a set of measurements, we can use:

Answer 31

1) R ≈ 4-6 s 2) s ≈R/4 or s≈ R/6 for large data set

Question 32

Measurement of how many standard deviations away from the mean

Answer 32

Z-score = x -x̄ / s

Question 33

What values would we indicate as outliers?

Answer 33

zscore that is: z\<-3 OR z\>3

Question 34

Measurement of how many measurements lie below the measurement of interest

Answer 34

Pth percentile

Question 35

the value of x which is larger than 25% and less than 75% of the ordered measurements.

Answer 35

Lower Quartile (Q1)

Question 36

The value of x which is larger than 75% and less than 25% of the ordered measurements.

Answer 36

Upper Quartile (Q3)

Question 37

The range of the “middle 50%” of the measurements

Answer 37

Interquartile Range

Question 38

Interquartile Range (IQR) equation

Answer 38

IQR = Q3-Q1

Question 39

Position of Q1

Answer 39

.25(n+1)

Question 40

Position of Q3

Answer 40

.75(n+1)

Question 41

If the position of Q1 or Q3 are not integers, find the quartiles by?

Answer 41

Interpolation (1st position # + .25/.75(2nd position # - 1st position #)

Question 42

Five Number Summary

Answer 42

Min Q1 Median Q3 Max

Question 43

Use the Five Number Summary to form a __ \_\_ to describe the __ of the distribtion and to detect \_\_\_.

Answer 43

Box Plot Shape Outliers

Question 44

Constructing a Box Plot 1) Calculate? 2) Draw horizontal line to represent? 3) Draw box using?

Answer 44

1) Q1, median, Q3, IQR 2) draw horizontal line to represent scale of measurement 3) draw box using Q1, median, Q3

Question 45

Constructing a Box Plot 1) Isolate Outliers by Calculating? 2) Equations?

Answer 45

1) Lower and Upper Fence 2) Lower Fence: Q1-1.5 IQR Upper Fence: Q3+1.5 IQR

Question 46

Measurements beyond the __ and __ \_\_ is/are outliers and are marked \_\_.

Answer 46

upper or lower fence marked (\*)

Question 47

Generic Box Plot Diagram

Answer 47

Question 48

Draw “whiskers” connecting the __ and __ \_\_ that are NOT __ to the box.

Answer 48

largest and smallest measurements outliers

Question 49

Box Plot of symmetric distribution

Answer 49

Median line in center of box and whiskers of equal length

Question 50

Box Plot - skewed right

Answer 50

Median line left of center and long right whisker

Question 51

Box Plot - skewed left

Answer 51

Median line right of center and long left whisker