Frequency Distribution Table
After the collecting stage, the data must be organized. A frequency distribution
table can be used. It is used to rank the
disorganized data from the highest to the lowest. A frequency distribution table
is an organized tabulation of the number of
individual scores located in each category on the scale of measurement. It
contains at least two columns - one for the score categories (X) and another for
the frequencies (f).
A frequency distribution can be represented in a number of ways.
Group frequency table; Regular frequency table
Group frequency graph -
The bar graph; Histogram
The bar graph is used when the data or measurements are from a nominal or an
Histogram - Interval or Ratio data
Polygon - Interval or Ratio data
Group frequency distribution is used when the original scale of measurement
consists of more categories than can be listed in a regular table, 20 or more
categories is generally considered too much. The Simplest and the most complete way to present a set of N= 7 scores is to
list each individual score. This will call for the use of a polygon.
A grouped frequency distribution table is needed when the range of scores is
large, causing a regular frequency table to have too many entries in the
score categories (X column). The guidelines for a group frequency table includes:
Striving for approximately 10 rows in the table;
Interval width of 2,5,10,20,50,100 should be used - depending upon the number of
The first (lowest) value of each interval should be a multiple of the interval
List all intervals without skipping any. The top interval should contain the
highest observed X value and the bottom interval should contain the lowest
observed X value.
The real limits for a score are the boundaries located halfway between the score
and the next higher (or lower) score.
Example: Organize the data below into a frequency distribution table and show
percentage of each category.
8, 9, 8, 7, 10, 9, 6, 4, 9, 8,
7, 8, 10, 9, 8, 6, 9, 7, 8, 8
If the data covers a wide range of values it is reasonable to
group them in a frequency table.
Draw a group distribution table from the data below.
|12 - 13
||11.5 - 13.5
|10 - 11
||9.5 - 11.5
|8 - 9
||7.5 - 9.5
|6 - 7
||5.5 - 7.5
|4 - 5
||3.5 - 5.5
Researches prefer to describe distributions by talking about the
"shape", central tendency", and "variability".
- Central tendency measure where the center of the distribution is located.
- Variability tells whether the scores are spread or clustered together.
Finding a single score that is the most representative of a group of data is
the goal here. Three commonly used technique for measuring central tendency are
the mean, the median, and the mode.
- The mean is the same as the average.
- The median is the item that occupies the very middle position when the
data (score) is ranked from the smallest to the largest.
- The mode is the number with the highest frequency ( occurs often).
There are several ways to find the mean depending on the type of data.
Given the population 3,7,4,6. Find the mean, µ:
x = 3+7+4+6 = 20
N = 4
Given the sample, 2,4,6,8,5,11. Find the mean
COMPUTING MEAN FROM FREQUENCY DISTRIBUTION TABLE
When a frequency table is given, the mean can be found from the formula:
It is used instead of the mean when
- there is a skewed distribution.
- it is an open-ended distribution.
- there is an undetermined score.
- there is an ordinal scale.
- the median is not affected by extreme numbers.
Determining the median:
- when the sample size is odd - arrange the data in ascending or descending
order and take the middle score.
- When the sample size is even - arrange the data in ascending or descending
order and take the two middle numbers, add them up and divide the sum by 2.
The score or group with the highest frequency.
- It is preferred when the scores are measured on a nominal scale.
- It can be used on all scales.
Central Tendency and the shape of the distribution:
All 3 measures of central tendency relate in a way. All 3 can have the same
value under the same circumstances. The shape of the distribution determines the
NEW TERMS AND CONCEPTS
||A tabulation of the number of individuals in each
on the scale of measurement.
|Grouped frequency distribution
||A frequency distribution where scores are
intervals rather than listed individual values.
||A group of scores in a grouped frequency distribution.
|Upper real limit
||The boundary that separates an interval from
|Lower real limit
||The boundary that separates
an interval from the next lowest
||A graph showing a bar above each score
or interval so that
the height of the bar corresponds to
the frequency and width extends the
||A graph showing a bar above each score or inte
the height of the bar corresponds to
the frequency. A space is left
between adjacent bars.
||A graph consisting of a line that connects a series
A dot is placed above each score or interval
so that the height of the dot
corresponds to the frequency.
||A distribution where the left-hand side is a mirror
the right-hand side.
|Positively skewed distribution
||A distribution where the scores pile up on the
left side and
taper off to the right.
|Negatively skewed distribution
||A distribution where the scores pile up on
the right side
and taper off to the left.
|Tail(s) of a distribution
||A section on either side of a distribution
frequency tapers down toward zero
as the X values become more extreme.
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