z – Score Percentiles Quartiles

A standardized value A number of standard deviations a given

value, x, is above or below the mean z = (score (x) – mean)/s (standard

deviation) A positive z-score means the value lies

above the mean A negative z-score means the value lies

below the mean Round to 2 decimals

Score (x) = 130 Mean = 100 s = 15 z = (score (x) – mean)/s (standard

deviation) z = (130 - 100)/15 (standard deviation)

o = 30/15, = 2o The score of 130 lies 2 standard deviations

above the mean (positive z means above the mean)

Score (x) = 85 Mean = 100 s = 15 z = (score (x) – mean)/s (standard

deviation) z = (85- 100)/15 (standard deviation)

o = -15/15, = -1o The score of 85 lies 1 standard deviation

below the mean (negative z means below the mean)

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

P1, P2, P3, P4, …P99 Percentile of value x = number of values

< x divided by the total number of values * 100 (for percent)

Round to nearest whole number

Percentile of value x = number of values < x divided by the total number of values * 100 (for percent)

Find the percentile for the value of 18

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Find the percentile for the value of 18 Percentile of 18 = 10 (numbers less than

18) 18 (total number of

values) Percentile of 18 = .55556 * 100 = 56% This means that the value of 18 is the

56th percentile

Converting a percentile into a data value L = the locator that gives the position of

the value k = percentile Find the 20th percentile, P20

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Find the 20th percentile, P20

Compute L L = k/100 * n L = 20/100 * 18 L = .20 * 18 = 3.6 When L is not a whole number, round up

instead of off L = the 4th value, which is 7 in the table

L = the 4th value, which is 7 in the table This means that the 20th percentile is the

value 7 and about 20% of the values are below the value 7 and about 80% of the values are above the value 7.

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Converting a percentile into a data value L = the locator that gives the position of

the value k = percentile Find the 50th percentile, P50

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Find the 50th percentile, P50

Compute L L = k/100 * n L = 50/100 * 18 L = .50 * 18 = 9 When L is a whole number, the value of

the k percentile is midway between the Lth value and the next sorted value (take the average of the two values).

L = the 9th value, which is 16 in the table Take this value plus the next sorted

value, which is also 16, and calculate the average

Here, the 9th percentile is 16.5 6 6 7 9 10

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Measures of location which divide a set of data into four groups with about 25% of the values in each group

Q1, Q2, Q3, Q4

Q1 = P25 = First quartile, the bottom 25% Q2 = P50 = Second quartile, same as the

median Q3 = P75 = Third quartile, the upper 25%

Finding Q1 is the same as finding P25

L = k/100 * n L = 25/100 * 18 L = .25 * 18 = 4.5, or the 5th value In the table, the 5th value is 9 So, Q1 = 9

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