Quantitative data in statistics exhibits some general characteristics that constitute the ideology of descriptive measures.
Statistics Solutions is the country's leader in descriptive statistics and dissertation statistics. Contact Statistics Solutions today for a free 30-minute consultation.
There are four different forms of descriptive measures.
The first form of descriptive measures is the measure of central tendency, which is also called the averages.
The second form of descriptive measures is the measure of variation or dispersion.
The third form of descriptive measures is the measure of skewness.
The fourth form of descriptive measures is the measure of kurtosis.
The first form of descriptive measures consists of five descriptive measures, namely Arithmetic Mean, Median, Mode, Geometric Mean and Harmonic Mean.
There are some characteristics that have been put forth by Professor Yule regarding descriptive measures. They are as follows:
1. Descriptive measures should be rigidly defined.
2. Descriptive measures should be less complicated and easy to calculate.
3. The descriptive measures being calculated must be based upon all the observations under consideration.
4. The descriptive measures must be applicable for further mathematical treatment.
5. The descriptive measures must not get affected by the fluctuations of the sampling.
6. The descriptive measures should not get affected by extreme values.
The descriptive measure called the arithmetic mean is defined as the sum of the set of the observations that is divided by the number of that particular set of observations. This descriptive measure satisfies the first five properties laid down by Professor Yule. The biggest disadvantage of this descriptive measure is that it can’t be used in the case of qualitative data and it is also affected by extreme values.
The descriptive measure called the median is defined as that value of the variable which divides the data under consideration into two equal parts. This descriptive measure satisfies the first two and the sixth property put forth by Professor Yule. This descriptive measure can be used in the case of qualitative data, but this descriptive measure cannot be measured quantitatively.
The descriptive measure called mode is defined as the value that occurs most of the time in a particular set of observations. This descriptive measure satisfies the second and the last property that has been put forth by Professor Yule. It is that type of descriptive measure that is used in obtaining an ideal size in business forecasting, etc.
The descriptive measure called the geometric mean is defined as the nth root of the product of the set of the observations under consideration. The basic disadvantage of this type of descriptive measure is that it can neither be easily understood nor be calculated by the person who does not have a mathematical background. This descriptive measure satisfies the first, third, fourth and fifth property put forth by Professor Yule.
The descriptive measure called the harmonic mean is defined as the reciprocal of the arithmetic mean of the reciprocals of the given values provided that none of the observations are zero. The basic disadvantage of this type of descriptive measure is that it cannot be easily understood or be calculated by a person who does not have a mathematical background. This descriptive measure satisfies the first, third, fourth and fifth property put forth by Professor Yule.
The second form of descriptive measure is classified into two categories.
The first category is used in expressing the spread of the observations with respect to the distance that exists between the values of the selected observations. This includes things like range, inter-quartile range, etc.
The second category is used in expressing the spread of the observations with respect to the average of the deviations of the observations for some central value. This includes things like mean, deviation, standard deviation, etc.
The third form of descriptive measure consists of three coefficients of skewness, namely Professor Karl Pearson’s coefficient of skewness, Professor Bowley’s coefficient of skewness and the coefficient of the skewness that is based on the moments.
The fourth form of descriptive measure gives an idea about the flatness or peakedness of the frequency curve. If the curve is neither flat nor peaked, then the descriptive measure concludes that it is a normal curve or a mesokurtic curve. If the curve is flatter than the normal curve, then the descriptive measure concludes that it is a platykurtic curve. If the curve is more peaked, then the descriptive measure concludes that it is a leptokurtic curve.
