Health Stats Chapter 2

Class Midpoint

Divide the sum of the two limits (or the two boundaries) of a class by 2 to obtain the class midpoint Example: the class limits of the lowest interval (5-9) have class boundaries of 4.5 to less than 9.5. The class midpoint is 7 (5 + 9 = 14 divided by 2 = 7).

Class Limit

Each class will have a lower limit and an upper limit Any convenient number, equal to or less than the smallest value in the data set, can be used to set the lower limit for the first class The class width determines the upper limit The remainder of the class limits are set in sequence until all scores are included Example: 25-29 (25 is the lower class limit and 29 is the upper class limit)

Rank

Indicates relative status in a group The rank of a score indicates its position in a series when all scores have been arranged in order of magnitude A rank of 30 indicates that the score is 30th in the distribution when all scores were ranked in order of magnitude

Class Width

It is preferable to have the same width for all classes To approximate class width, divide the range by the number of classes desired The more detailed the interpretation one needs, the smaller the class interval Example: 25-29, 20-24, 15-19 (the class width is 5)

Importance of Percentiles

A raw score may not be meaningful, but when compared to the rest of the group, the percentile is an indication as to how the performance measured to the rest of the group. Percentile scores are not equally divided up and down a percentile scale.

Quartiles

divide the data into four equal parts (25%, 50%, 75%, 100%). The middle score in the distribution is referred to as the median and the score at the 2nd quartile mark (equivalent to the 5th decile) is also the median of the distribution

Deciles

divide the data into ten equal parts. The first decile includes 1/10 or 10% of the data in the distribution; the second decile another tenth (20%) and so on. There are ten deciles in a distribution

Percentiles

divide the distribution into 100 equal segments. The data should be ranked in increasing order to compute percentiles.

Percentile Score

represents the score that one has to attain to reach a specific percentile. To rank at the 90th percentile, an individual may need a score of 67.

Percentile Rank

the percentile for a specific score. Someone who scores a 67 on a test may rank at the 90th percentile; however, a score of 15 on another test may also be ranked at the 90th percentile.

Frequency Distribution Table

A frequency distribution table generally contains a score column, a frequency column, and a cumulative frequency column. The number of classes should generally be from 5 to 15 Include all scores in the distribution—the entire range Each data entry should fall into only one category An equal class size is preferred

Rules for Subsequent Computations

Desired number of class intervals (15 or between 12 and 20) Preferred class size (1,2,3,5,7,10,15 or any higher multiple of 5)

General Rules for Creating a Frequency Distribution

Determine range Establish the number of class intervals recommend at least 5, but no more than 20, with 15 being preferred Set class limits Lower limit a multiple of interval size Multiple of highest score appears as the middle score of the interval Multiples of 5 or 10

Class Boundaries

The midpoint of the upper limit of one class and the lower limit of the next class; 0.5 below the lower class limit to 0.4 The smaller number is the lower class boundary and the larger number is the upper class boundary Also called real class limits, actual class limits, true class limits Example: Class interval of 25 to 29 inches = class boundaries of 24.5 up to 29.5

Cumulative Frequency

The sum of the frequencies starting at the lowest interval (at the bottom) and including the frequencies within that interval. Next, add in successive class frequencies from the bottom to the top The accumulation of frequencies results in the top interval containing the total number in the distribution

Relative Frequency and Percentage

To calculate the relative frequency for a class, divide the frequency for that class by the sum of all frequencies (total scores in the distribution) The percentage is determined by multiplying the relative frequency by 100