Download Arithmetic mean for grouped data

Descriptive statistics is a branch of statistics that denotes any of the many
techniques used to summarize a set of data. The techniques are commonly classified as:
A. Graphical description in which we use graphs to summarize data.
B. Tabular description in which we use tables to summarize data.
C. Summary statistics in which we calculate certain values to summarize data.
A. Graphical representation of data - we can make a graph of the
data. For example
1. bar graph
2. histogram
3. frequency polygon
4. scatter diagram
B. Tabular representation of data - we can summarize data by
making a table of the data. In statistics we call these tables frequency distributions
1.
2.
3.
4.
5.
6.
Simple frequency distribution (or it can be just called a frequency distribution).
Cumulative frequency distribution.
Grouped frequency distribution.
Cumulative grouped frequency distribution.
Relative frequency distribution
Cumulative relative Distribution.
C. Summary statistics are used to summarize a set of observations. We can
use a single number to represent many numbers. Statisticians commonly try to describe
the observations in
I.
II.
III.
IV.
I.
Measure of central tendency
Measure of statistical dispersion or variation or spread.
Measure of the shape of the distribution like skewness
Measure of position.
A list of measures of central tendency
There are several different kinds of calculations for central tendency; the kind of
calculation that should be used depends on the type of data (level of measurement) and
purpose for which the central tendency is being calculated:
1
Arithmetic mean
 Arithmetic mean for discrete data
o Sample Mean
o Population mean
 Arithmetic mean for grouped data
2.
Median


3.
Median for grouped data
Median for discrete data.
Mode


Mode for grouped data
Mode for discrete data
4.
Geometric mean
5.
Harmonic mean
6.
Weighted mean
7.
Truncated mean or trimmed mean
8.
Midrange
9.
Winsorized mean
10. Mid hinge.
II. A list of measures of dispersion or variation or
Spread
1
Range
1
Variance


3.
Sample Variance
Population Variance
Standard Deviation

Population standard deviation

4.
5.
Sample standard deviation.
Quartile deviation
Five Number summary
III. A list of measures of shape of the distribution.
1.
Symmetrical Distribution
2.
Asymmetrical Distribution
 Skewed Distribution



Positively Skewed Distribution
Negatively skewed Distribution
Moderately skewed and unimodal Distribution.
IV. A list of measures of position
1. Sorting the data.
2. Percentiles, deciles and quartiles.
3. Interquartile range
4. Box and whisker plots.