TOPIC THREE
STATISTICAL TREATMENT OF DATA
3.0 Introduction
Statistics enables analytical chemist to accept conclusions that have high probability of being
correct and to reject conclusions that are doubtful. Hence statistical treatment of data helps in
ascertaining the significance and integrity of values reported.
Objectives
At the end of this unit, students should be able to:
i. List appropriate statistical tools available for data handling;
ii. Define various statistical terms and state their importance; and
iii. Use various statistical tools in interpreting data and arrive at a safe conclusion.
3.1 Ways of Expressing Precision
Statistics has enabled scientists to accept or reject conclusions on figures depending on the
degree of precision carried or attached by the numerical report.
Precision is defined as the degree of agreement between replicate measurements of the same
quantity. There are various tools that are used in expressing the precision.
These include: average deviation, variance, standard deviation etc.
3.1.1 Average Deviation (A.D)
It is one of the methods of showing dispersion or way of ascertaining the deviation from the
central values. It is otherwise called Mean Deviation. It helps further in measuring distribution
that is based upon all the items in a distribution.
| ̅| | |
Where;
dx = deviation from mean
n = number of observations
x = observation
̅ = sample mean
1
, As with accuracy, precision measurement such as average deviation can be expressed as an
absolute figure or as a relative figure (%, pph, ppt etc)
3.1.2 Variance
This is simply called mean square deviation. Variance is an important measure in the quantitative
analysis of data. It helps in isolating the effect of various factors. It also helps in developing
some statistical theories.
Variance is one of the most important concepts of statistics. It is the measure of dispersion of a
set of data. It indicates how far the different values of a set of data are spread. Variance is the
measurement of deflection of values from its mean. Variance is the average of squared
differences of each value from mean of the data.
There is one difference between variance and standard deviation that standard deviation is
defined as the square root of variance. Variance is denoted by square of a Greek letter sigma
(σ2).
The formulas for variance are given below.
Variance formula for population data is as follows:
∑ ̅
Variance formula for sample data is as follows:
∑ ̅
Where;
σ2 = Variance
x = Item given in the data
̅ = Mean of the data
n = number of observations
3.1.3 Standard Deviation (SD)
2
STATISTICAL TREATMENT OF DATA
3.0 Introduction
Statistics enables analytical chemist to accept conclusions that have high probability of being
correct and to reject conclusions that are doubtful. Hence statistical treatment of data helps in
ascertaining the significance and integrity of values reported.
Objectives
At the end of this unit, students should be able to:
i. List appropriate statistical tools available for data handling;
ii. Define various statistical terms and state their importance; and
iii. Use various statistical tools in interpreting data and arrive at a safe conclusion.
3.1 Ways of Expressing Precision
Statistics has enabled scientists to accept or reject conclusions on figures depending on the
degree of precision carried or attached by the numerical report.
Precision is defined as the degree of agreement between replicate measurements of the same
quantity. There are various tools that are used in expressing the precision.
These include: average deviation, variance, standard deviation etc.
3.1.1 Average Deviation (A.D)
It is one of the methods of showing dispersion or way of ascertaining the deviation from the
central values. It is otherwise called Mean Deviation. It helps further in measuring distribution
that is based upon all the items in a distribution.
| ̅| | |
Where;
dx = deviation from mean
n = number of observations
x = observation
̅ = sample mean
1
, As with accuracy, precision measurement such as average deviation can be expressed as an
absolute figure or as a relative figure (%, pph, ppt etc)
3.1.2 Variance
This is simply called mean square deviation. Variance is an important measure in the quantitative
analysis of data. It helps in isolating the effect of various factors. It also helps in developing
some statistical theories.
Variance is one of the most important concepts of statistics. It is the measure of dispersion of a
set of data. It indicates how far the different values of a set of data are spread. Variance is the
measurement of deflection of values from its mean. Variance is the average of squared
differences of each value from mean of the data.
There is one difference between variance and standard deviation that standard deviation is
defined as the square root of variance. Variance is denoted by square of a Greek letter sigma
(σ2).
The formulas for variance are given below.
Variance formula for population data is as follows:
∑ ̅
Variance formula for sample data is as follows:
∑ ̅
Where;
σ2 = Variance
x = Item given in the data
̅ = Mean of the data
n = number of observations
3.1.3 Standard Deviation (SD)
2
