 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 = ( )/15 (standard deviation) o = 30/15, = 2 o 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 = ( )/15 (standard deviation) o = -15/15, = -1 o 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  P 1, P 2, P 3, P 4, …P 99  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

 Find the percentile for the value of 18  Percentile of 18 = 10 (numbers less than 18) 18 (total number of values)  Percentile of 18 = * 100 = 56%  This means that the value of 18 is the 56 th percentile

 Converting a percentile into a data value  L = the locator that gives the position of the value  k = percentile  Find the 20 th percentile, P

 Find the 20 th percentile, P 20  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 4 th value, which is 7 in the table

 This means that the 20 th 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

 Converting a percentile into a data value  L = the locator that gives the position of the value  k = percentile  Find the 50 th percentile, P

 Find the 50 th percentile, P 50  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 L th value and the next sorted value (take the average of the two values).

 L = the 9 th 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 9 th percentile is

 Measures of location which divide a set of data into four groups with about 25% of the values in each group  Q 1, Q 2, Q 3, Q 4  Q 1 = P 25 = First quartile, the bottom 25%  Q 2 = P 50 = Second quartile, same as the median  Q 3 = P 75 = Third quartile, the upper 25%

 Finding Q 1 is the same as finding P 25  L = k/100 * n  L = 25/100 * 18  L =.25 * 18 = 4.5, or the 5 th value  In the table, the 5 th value is 9  So, Q 1 =