Question

Which one of the following is a false description?
1.In a moderately asymmetrical distribution, the empirical relationship between mean, mode and median suggested by Karl Pearson is $Mean - Mode = 3(Mean - Median)$.
2.Coefficient of variation is an absolute measure of dispersion.
3.Measure of skewness in the distribution of numerical values in the data set.
4.Kurtosis refers to the degree of flatness or peakedness in the region around the mode of a frequency curve.

Answer 1

Hint: Here, in the given question, we are given a description of a few statistical terms and we need to find which of the given description is false. We will first understand the concept of every description and then we will find out which of them is false.
1.In a moderately asymmetrical distribution, the empirical relationship between mean, mode and median suggested by Karl Pearson is $Mean - Mode = 3(Mean - Median)$.
We can express the relationship between mean, median and mode by Karl Pearson’s formula. It is defined as the distance between the mean and the median is about one-third the distance between the mean and the mode.
$ \Rightarrow Mean - Median = \dfrac{1}{3}\left( {Mean - Mode} \right)$
$ \Rightarrow 3\left( {Mean - Median} \right) = Mean - Mode$
Therefore, this description is true.

2.Coefficient of variation is an absolute measure of dispersion.
Let us understand the types of measures of dispersion. There are two types, that is, Absolute Measure of Dispersion and Relative Measure of Dispersion.
Let us see the types in Absolute Measure of Dispersion. These include range, variance, standard deviation, quartiles and quartile deviation, and mean and mean deviation.
From the above-mentioned absolute measure of dispersion, we can see that coefficient of variation is not a measure of dispersion but standard deviation is.
Therefore, this description is false.

3.Measure of skewness in the distribution of numerical values in the data set.
Skewness refers to a distortion or asymmetry that deviates from the symmetrical bell curve or normal distribution, in a set of data. So we can conclude that the given description is true.

4.Kurtosis refers to the degree of flatness or peakedness in the region around the mode of a frequency curve.
As we know kurtosis is the measure of the tailedness in the frequency distribution. Therefore, this description is true.

Thus, the correct option is 2.

Note:
To solve this type of question, one must know all the statistical terms to find the correct answer. Remember the below-written points:
In normal distribution mean=median=mode, but if one tail is longer than another, the distribution becomes skewed. These are sometimes called asymmetrical distributions.
Standard deviation (SD) is a measure of spread of data about the mean. It is the square root of the sum of squared deviation from the mean divided by the number of observations. We can represent SD as
$\sigma = \sqrt {\dfrac{{\sum {{{\left( {{x_i} - \mu } \right)}^2}} }}{N}} $ where N is the size of the population, ${x_i}$ is each value from the population and $\mu $ is the population mean.