2: Frequency Distributions, Percentiles, and Percentile Ranks

How to construct a grouped frequency distribution

1. find the lowest score and the highest score 2. find the range by subtracting the lowest score from the highest 3. Divide the range by 10 and by 20 to determine the largest and the smallest acceptable interval widths. Choose a convenient width (i) within these limits. 4. Determine the score at which the lowest (or highest) interval should begin. It should ordinarily be a multiple of the interval width 5. Record the limits of all class intervals, placing the interval containing the highest score value at the top. Make the intervals continuous and of the same width. 6. tally the scores ==> convert to frequency

Checklist for a grouped frequency distribution.

1. make sure class intervals are: - mutually exclusive - same width (i) - convenient width (2, 3, 4, 5, 10, 25, 50) - continuous throughout the dimension - about 10-20 categories 2. descending order 3. try to make the lower score limits multiples of the interval width (i)

percentile (point)

a point on the measurement scale below which a specified percentage of the cases in a distribution falls; any value of score ex. 81 is the 50th percentile

What is the difference between an ungrouped frequency distribution and a grouped frequency distribution?

an ungrouped frequency distribution retains the raw scores (shows frequencies individually) whereas a grouped frequency uses class intervals. The information lost between these (relatively speaking) is called grouping error.

What is the symbol for relative frequency?

as a proportion: rel f (propor.) as a percentage: rel f (%)

What is the symbol for cumulative percentage?

cum %

What is the symbol for cumulative frequency?

cum f

cum f

cumulative frequency

cum f (propor.)

cumulative frequency expressed as a proportion out of 1

cum f (percentile)

cumulative frequency expressed as a proportion out of 100

real (exact) limits of a score

extend from 1/2 of the smallest unit of measurement below the value of the score to 1/2 unit above

real (exact) limits of a score interval

extend from 1/2 the measurement unit below the lowest score to 1/2 the unit above the highest score.

apparent limits of a score interval

extend from the smallest unit of measurement in the interval to the largest (i.e. what you think it is)

relative cumulative frequency distribution

hows the proportion/percentage of cases that lie below the upper real limit of each class interval.

class intervals

in a frequency distribution, a range of values that are grouped together

How do you calculate the relative frequency expressed as a proportion?

sample: f/n population: f/N

raw scores

scores in their original form

cumulative frequency distribution

shows how many cases lie below the upper real limit of each class interval.

frequency distribution

shows the number of observations (frequency) for the possible categories or score values in a set of data

relative frequency distribution

shows the proportion (decimal) or percentage (%) of the total number of observations for the possible categories or score values in a set of data

ƒ

symbol for frequency

i

symbol for interval width

LL

symbol for the lower real limit of the interval of interest.

N

symbol for total number of cases in a population

n

symbol for total number of cases in a sample

range

the difference between the lowest score and the highest score

grouping error

the information lost by using organizing data into groups (class intervals) as opposed to retaining raw scores.

percentile ranks

the percentage of cases in a distribution that falls below a given point on the measurement scale; [0, 100] ex. 81 has a percentile rank of 50

how to construct an ungrouped frequency distribution.

2 columns: X; f descending order, skipping no values in between, Can include values beyond the range of values obtained if you want (I think) Ex. 100, 99, but cannot include values which are impossible to obtain Ex. 102, 101

When you group scores following the guide-lines, does it matter whether you start with the highest scores or the lowest scores?

No; if you make the lower apparent limits of each interval a multiple of the interval width, you will arrive at the same score intervals. Ex. IF 250-299, i=50 (note 250 is a multiple of 50); all intervals the same 250-849 AS IF 800-849, i=50 (note 800 is a multiple of 50).

What is the symbol for percentile (point)?

P