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Statistics

Sampling Distributions

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24 Terms

1
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Mean

  1. Sum of values

  2. Divide by # of values

<ol><li><p>Sum of values </p></li><li><p>Divide by # of values</p></li></ol><p></p>
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Median

Of ranked data:

If odd, position # of values +1 / 2

If even, average middle numbers

<p>Of ranked data:</p><p>If odd, position # of values +1 / 2</p><p>If even, average middle numbers</p>
3
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Mode

Most frequent

<p>Most frequent </p>
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Grouped mean

  1. The sum of all frequencies multiplied by the midpoints

  2. Divide by the number of values

<ol><li><p>The sum of all frequencies multiplied by the midpoints </p></li><li><p>Divide by the number of values</p></li></ol><p></p>
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Weighted mean

  1. The sum of the frequencies multiplied by the weights

  2. Divided by the sum of the weights

<ol><li><p>The sum of the frequencies multiplied by the weights</p></li><li><p>Divided by the sum of the weights</p></li></ol><p></p>
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Grouped mode

The most frequent interval

<p>The most frequent interval</p>
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Grouped median

The lower bound added onto the distance into the interval (use cumulative frequency to find this) divided by the frequency that is multiplied by the upper bound minus the lower bound

<p>The lower bound added onto the distance into the interval (use cumulative frequency to find this) divided by the frequency that is multiplied by the upper bound minus the lower bound</p>
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Deviation

The value minus the mean

<p>The value minus the mean</p>
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Standard Deviation

  1. The sum of the x values minus the mean, squared

  2. Divided by the number of values (minus one if sample)

  3. Square rooted

<ol><li><p>The sum of the x values minus the mean, squared</p></li><li><p>Divided by the number of values (minus one if sample)</p></li><li><p>Square rooted</p></li></ol><p></p>
10
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Variance

  1. The sum of the x values minus the mean, squared

  2. Divided by the number of values (-1 if sample)

<ol><li><p>The sum of the x values minus the mean, squared</p></li><li><p>Divided by the number of values (-1 if sample)</p></li></ol><p></p>
11
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First quartile, Q1, position

One quarter multiplied by the number of values plus one

<p>One quarter multiplied by the number of values plus one</p>
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Quartile or quartile position when not a whole number

Use lower number added onto the decimal multiplied by the higher number minus the lower number

<p>Use lower number added onto the decimal multiplied by the higher number minus the lower number </p>
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Second quartile, Q2 or median, position

One half multiplied by the number of values plus one

<p>One half multiplied by the number of values plus one</p>
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Third quartile, Q3, position

Three quarters multiplied by the number of values plus one

<p>Three quarters multiplied by the number of values plus one</p>
15
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Percentile

K percent times the number of values plus one

<p>K percent times the number of values plus one</p>
16
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Z-scores

  1. The value minus the mean

  2. Divided by the standard deviation

<ol><li><p>The value minus the mean</p></li><li><p>Divided by the standard deviation </p></li></ol><p></p>
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Values from z-scores

Mean plus the z-score multiplied by the standard deviation

<p>Mean plus the z-score multiplied by the standard deviation </p>
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Interquartile range

Q3 - Q1

<p>Q<sub><sup>3</sup></sub> - Q<sub>1</sub></p>
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Outlier tests

Q1 - 1.5(IQR)
Q3 + 1.5(IQR)

<p>Q<sub>1</sub> - 1.5(IQR)<br>Q<sub><sup>3</sup></sub> + 1.5(IQR)</p>
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Within standard deviation

Mean minus standard deviation and mean plus standard deviation

<p>Mean minus standard deviation and mean plus standard deviation </p>
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Grouped standard deviation

  1. The sum of the frequencies then times the midpoints subtract the mean

  2. Squared

  3. Divided by number of values (minus one if sample)

  4. Square rooted

<ol><li><p>The sum of the frequencies then times the midpoints subtract the mean </p></li><li><p>Squared</p></li><li><p>Divided by number of values (minus one if sample)</p></li><li><p>Square rooted</p></li></ol><p></p>
22
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Stratified samples

  1. Take the size of the group divided by the total number of people

  2. Multiply by the desired sample size

<p></p><ol><li><p>Take the size of the group divided by the total number of people </p></li><li><p>Multiply by the desired sample size</p></li></ol><p></p>
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Bell marks

  1. Find z-score

  2. Take the desired mean and add the desired standard deviation multiplied by the z-score

<ol><li><p>Find z-score</p></li><li><p>Take the desired mean and add the desired standard deviation multiplied by the z-score</p></li></ol><p></p>
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Midpoint

  1. Lower limit plus upper limit​

  2. Divided by two

<ol><li><p>Lower&nbsp;limit plus upper&nbsp;limit​</p></li><li><p>Divided by two</p></li></ol><p></p>

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