# PSY201H1 Chapter Notes - Chapter 3: Percentile Rank, Cumulative Frequency Analysis, Frequency Distribution

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Understanding Statistics Chapter 3

PSY201

Grouping Scores

Frequency distribution of grouped scores

How scores are to be presented when there are many so that we can see the shape

of the distribution

To construct a frequency distribution of grouped scores

Find the range of scores

Highest sore minus the lowest score

Determine the width of each class interval (i)

i= range/# of class intervals

Remember to count EACH unit, so 50-55 isn’t 5 units wide, it’s 6 units wide

List the limits of each class interval, placing the interval containing the lowest

score value at the bottom

Start with the lowest, which must contain the lower limit of the interval

Make the lower limit divisible by i! So if the lowest unit is 42, start with 40 if

the i is 5 or 10

Tally the raw scores into the appropriate class intervals

Add the tallies of each interval to obtain the interval frequency

Relative Frequency, Cumulative Frequency, and Cumulative Percentage Distributions

Relative frequency distribution

Indicates the proportion of the total number of scores that occurs in each interval

Relative frequency = f/N [frequency divided by total number of scores]

Cumulative frequency distribution

Indicates the number of scores that fall below the upper limit of each interval

Add the frequency of that interval to the frequencies of all the intervals below it

Cumulative percentage distribution

Indicates the percentage of scores that fall below the upper real limit of each

interval

Convert cumulative frequencies to cumulative percentage

cum%=[(cumf)/N] X100

Percentiles

A percentile, or percentile point, is the value on the measures scale below which a

specified percentage of scores in the distribution fall

A measurement of relative standing, and to compare an individual score to that of a

reference group

Notation: for 50th percentile point, we write P50

Means: Value below which 50% of the other values fall

To find a percentile point

Determine the frequency of the scores below the percentile point = cumfp

cumfp= (% of scores below this percentile point) XN

For example, if there are 70 scores:

cumfp = (.50) X 70 = 35

Determine the lower real limit of the interval containing the percentile point

XL = real lower limit

Can be done by comparing the cumfp with the cumulative frequency for each

interval

Determine the number of additional scores we must acquire in the interval to reach

the percentile point

Number of additional scores = cumfp-cumfL

cumfL= frequency of scores below the lower real limit of the interval

containing the percentile point

Determine the number of additional units into the interval we must go to acquire

the additional number of units

Additional units = (number of units per score) X Number of additional units

(i/fi) X number of additional units

fi is the number of scores in the interval

i/fi is the number of units per score for the interval

Percentile Rank

Percentile rank is a score is the percentage of scores with values lower than the score in

question

Equation = {[cumfL + (fi/i)(X-XL)]N} X100

Graphing Frequency Distribution

Bar Graph

Best for nominal or ordinal data

Similar to a histogram, but there is a space between each bar that shows the

separation of the categories

Histogram

Best for interval or ratio data

Similar to a bar graph, but there is no space between each bar, just a line that shows

the real limit of the unit

Frequency Polygon

Best for interval or ration data

Instead of bars, there are points at the intervals and a line that connects each of the

dots

Cumulative Percentage Curve

Symmetrical

When folded in half, the two sides collide

If a curve is not symmetrical, it is skewed

Skewed

Positively skewed

When most of the scores occur at the lower values of the horizontal axis and

the curve tails off towards the higher end

Negatively skewed

When most of the scores occur at the higher values of the horizontal axis and

the curve tails off towards the lower end