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Statistics > Chapter 3: Describing, Exploring, and Comparing Data > Flashcards

Chapter 3: Describing, Exploring, and Comparing Data Flashcards

1
Q

Measure of Center

A

the value at the center or middle of a data set

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2
Q

Arithmetic Mean (Mean)

A

the measure of center obtained by adding the values and dividing the total by the numbers of value. What most people call an average

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3
Q

median

A

the middle value when the original data values are arranged in order of increasing (or decreasing) magnitude

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4
Q

Are median values affected by extreme values?

A

No, they are resistant measures of the center.

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5
Q

How is the median found for a data set that has an odd number of values?

A
  1. Sort the values 2. The median is the number located in the exact middle of the list.
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6
Q

How is the median found for a data set that has an even number of values?

A
  1. Sort the values 2. The median is found by computing the mean of the two middle numbers.
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7
Q

mode

A

the value that occurs with the greatest frequency

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8
Q

bimodal

A

two data values occur with the same greatest frequency

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9
Q

multimodal

A

more than data values occur with the same greatest frequency

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10
Q

no mode

A

no data value is repeated

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11
Q

Which measure of central tendency can be used with nominal data.

A

Only mode

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12
Q

midrange

A

the value midway between the maximum and minimum values in the original data set

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13
Q

How is the midrange calculated?

A

(max value + min value)/2

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14
Q

What is the range of a set of data values?

A

The difference between the max data value and the min data value.

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15
Q

How is the range of a set of data values calculated?

A

range= (max value) - (min value)

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16
Q

What is the standard deviation of a set of sample values?

A

A measure of how much data values deviate from the mean.

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17
Q

Can the value of a standard deviation be negative?

A

NO!

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18
Q

What units are standard deviations expressed in?

A

The units are the same as the units of the original data values.

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19
Q

What is the range rule of thumb for understanding standard deviation?

A

For many data sets, the vast majority (such as 95%) of sample values lie within two standard deviations of the mean.

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20
Q

How are “usual” values in a data set determined using the range rule of thumb?

A

(mean)+/-2*(standard deviation)

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21
Q

Using the range rule of thumb, how are standard deviations roughly estimated from a collection of known samples?

A

range/4

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22
Q

variance

A

a measure of variation equal to the square of the standard deviation

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23
Q

Why is the sample variance s^2 an unbiased estimator of the population variance?

A

because the values of s^2 tend to target the value of population variance instead of systematically tending to overestimate or underestimate population variance.

24
Q

What is the empirical rule?

A

For data sets having a distribution that is approximately bell shaped, the following properties apply: ~68% of all values fall with in 1 standard deviation of the mean; ~95% of all values fall within 2 standard deviations of the mean; ~99.7% of all values fall within 3 standard deviations of the mean.

25
Q

What is Chebyshev’s Theorem?

A

The proportion (or fraction) of any set of data lying within K standard deviations of the mean is always at least 1-1K^2, where K is any positive number greater than 1.

26
Q

Using Chebyshev’s Theorem, what does K=2 mean?

A

At least 3/4 (or 75%) of all values lie within 2 standard deviations of the mean.

27
Q

Using Chebyshev’s Theorem, what does K=3 mean?

A

At least 8/9 (or 89%) of all values lie within 3 standard deviations of the mean.

28
Q

variance

A

a measure of variation equal to the square of the standard deviation

29
Q

Why is the sample variance s^2 an unbiased estimator of the population variance?

A

because the values of s^2 tend to target the value of population variance instead of systematically tending to overestimate or underestimate population variance.

30
Q

What is the empirical rule?

A

For data sets having a distribution that is approximately bell shaped, the following properties apply: ~68% of all values fall with in 1 standard deviation of the mean; ~95% of all values fall within 2 standard deviations of the mean; ~99.7% of all values fall within 3 standard deviations of the mean.

31
Q

What is Chebyshev’s Theorem?

A

The proportion (or fraction) of any set of data lying within K standard deviations of the mean is always at least 1-1K^2, where K is any positive number greater than 1.

32
Q

Using Chebyshev’s Theorem, what does K=2 mean?

A

At least 3/4 (or 75%) of all values lie within 2 standard deviations of the mean.

33
Q

Using Chebyshev’s Theorem, what does K=3 mean?

A

At least 8/9 (or 89%) of all values lie within 3 standard deviations of the mean.

34
Q

What is the coefficient of variation?

A

For a set of nonnegative sample or population data, expressed as percent, CV describes the standard deviation relative to the mean.

35
Q

How is the coefficient of variation calculated?

A

cv= (standard deviation/the mean) *100

36
Q

What are measures of relative standing?

A

Numbers showing the location of data values relative to the other values within a data set.

37
Q

In which ways are measures of relative standing used?

A

To compare values from different data sets or to compare values within the same data set.

38
Q

Name 4 examples of measures of relative standing.

A

z scores, percentiles, quartiles, and boxplots

39
Q

What is a z score?

A

The number of standard deviations that a given value x is above or below the mean.

40
Q

How are z scores determined?

A

z= (x-the mean)/standard deviation; round score to 2 decimal places

41
Q

Whenever a value is less than the mean, is its z-score positive or negative?

A

Negative

42
Q

What are ordinary z-score values?

A

-2<=2

43
Q

What are unusual z-score values?

A

zscore< -2 or zscore>2

44
Q

What are percentiles?

A

Measures of location that divide a set of data into 100 groups with about 1% of the values in each group.

45
Q

How is the percentile of a data value found?

A

(# of values less than x/ total # of values) *100

46
Q

How is a percentile converted to a data value?

A

L=(k/100)*n, where n=total number of values in the data set, k=percentile being used, L=locator that gives position of a value, Pk= kth percentile

47
Q

How is Pk found with a “L” value that is a whole number?

A

By adding the Lth value and the next value and dividing the total by 2.

48
Q

How is Pk found with a “L” value that is not a whole number?

A

By rounding L up to the next larger whole number.

49
Q

What are quartiles?

A

Measures of location, denoted Q1, Q2, and Q3, which divide a set of data into 4 equal parts with about 25% of the values in each group.

50
Q

Q1

A

separates the bottom 25% of sorted values from the top 75%

51
Q

Q2

A

same as the median; separates the bottom 50% of sorted values from the top 50%

52
Q

Q3

A

separates the bottom 75% of sorted values from the top 25%

53
Q

What is a interquartile range (IQR)?

A

Q3-Q1

54
Q

What is a semi-interquartile range?

A

(Q3-Q1)/2

55
Q

What is a midquartile?

A

(Q3+Q1)/2

56
Q

How is the 10-90 percentile range determined?

A

P90-P10

57
Q

What is a boxplot?

A

A graph of a data set that consists of a line extending from the minimum value to the maximum value, and a box with lines drawn at Q1, the median, and Q3.

Statistics (4 decks)

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