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STATS 160 > Chapter 2 - Describing Data with Numerical Measures > Flashcards

Chapter 2 - Describing Data with Numerical Measures Flashcards

1
Q

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

A

numberical measures

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2
Q

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

A

Parameter

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3
Q

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

A

Statistic

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4
Q

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

A

Measure of Center

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5
Q

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

A

MEAN

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6
Q

Sample Mean

A

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

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7
Q

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

A

µ (mew)

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8
Q

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

A

MEDIAN

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9
Q

Position of the Median (equation)

A

.5(n +1)

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10
Q

The measurement which occurs most frequently

A

Mode

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11
Q

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

A

mean, median

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12
Q

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

A

median

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13
Q

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

A

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

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14
Q

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

A

Measure of Variability

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15
Q

Difference between the largest and smallest measurements.

A

Range (R)

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16
Q

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

A

Variance

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17
Q

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

A

N, µ

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18
Q

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

A

(n-1)

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19
Q

Variance of a Population (equation)

A
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20
Q

Variance of a Sample (equation)

A
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21
Q

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 __ __.

A

1) Scale of the Measurements
2) Standard Deviation

22
Q

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

A
23
Q

The value of s is ALWAYS ?

A

positive

24
Q

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

A

variability of the data set.

25
Q

Calculational Formula for Sample Variance

A
26
Q

Definition Formula for Sample Variance

A
27
Q

Tchebysheff’s Theorem

A

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.

28
Q

Tchebysheff’s Theorem

1) If k=2?
2) If k=3?

A

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.

29
Q

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.

A

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

30
Q

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

A

ALL

31
Q

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:

A

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

32
Q

Measurement of how many standard deviations away from the mean

A

Z-score = x -x̄ / s

33
Q

What values would we indicate as outliers?

A

zscore that is:

z<-3 OR z>3

34
Q

Measurement of how many measurements lie below the measurement of interest

A

Pth percentile

35
Q

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

A

Lower Quartile (Q1)

36
Q

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

A

Upper Quartile (Q3)

37
Q

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

A

Interquartile Range

38
Q

Interquartile Range (IQR) equation

A

IQR = Q3-Q1

39
Q

Position of Q1

A

.25(n+1)

40
Q

Position of Q3

A

.75(n+1)

41
Q

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

A

Interpolation

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

42
Q

Five Number Summary

A

Min

Q1

Median

Q3

Max

43
Q

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

A

Box Plot

Shape

Outliers

44
Q

Constructing a Box Plot

1) Calculate?
2) Draw horizontal line to represent?
3) Draw box using?

A

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

45
Q

Constructing a Box Plot

1) Isolate Outliers by Calculating?
2) Equations?

A

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

Upper Fence: Q3+1.5 IQR

46
Q

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

A

upper or lower fence

marked (*)

47
Q

Generic Box Plot Diagram

A
48
Q

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

A

largest and smallest measurements

outliers

49
Q

Box Plot of symmetric distribution

A

Median line in center of box and whiskers of equal length

50
Q

Box Plot - skewed right

A

Median line left of center and long right whisker

51
Q

Box Plot - skewed left

A

Median line right of center and long left whisker

STATS 160 (8 decks)

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