What do you mean by qualitative data set, quantitative data set, measures of asymmetrical distributions, standard deviation of the data set, percentiles quartiles and deciles, nominal distribution, differentiate between empirical rule and chebyshevs rule, Chebyshev’s rule

 

a.      What do you mean by qualitative data set?

 

 

Qualitative dataset: 

 It generally involves Non-numerical parameters/ responses, as in the name it deals with Quality but not quantity.

 

a.      What do you mean by quantitative data set?

 

The quantitative data is defined as the value of data in the form of counts or number where each data set has an unique numerical value associated with it.

For example, height, weight, number of students in a university etc.

 

a.      What do you mean by measures of asymmetrical distributions?

Asymmetrical Distribution:

·         It is a situation in which values of variable occur at irregular frequencies and the mean, median and mode occurs at different points.

·         Skewness is a measure of the asymmetry of the probability distribution of real values random variable about its means.

a.      What do you mean by standard deviation of the data set?

          A standard deviation is a statistic that measures the dispersion of a dataset relative to its mean and is calculated as the square root of the variance. The standard deviation is calculated as the square root of variance by determining each data point's deviation relative to the mean.

a.      What do you mean by percentiles quartiles and deciles?

Percentiles

                  Percentiles divide the series into 100 parts. There are 99 percentiles known as P1, P2, and P3......P98, P99 which divide the series into 100 parts.

Quartiles:

              Quartiles divide the series into 4 parts. There are 3 quartiles resembled as Q1, Q2, and Q3 which divide the series into 4 parts.

Deciles:

             Deciles divide the series into 10 parts. There are 9 deciles resembling as D1, D2, D3, D4, D5, D6, D7, D8, and D9 which divide the series into 10 parts.

a.      To describe the nominal distribution,

 

Any distribution is said to be nominal if it is bell shaped with equal tails mean = median = mode. The curve at nominal distribution is mesokwitic with zero skewness.

 

b.      To differentiate between empirical rule and chebyshevs rule.

 

Empirical Rule:  Empirical rule is 68 – 95 – 99.7. this tells us that empirical 68% of data lies within 10 limits and 95 % data lies between 20 limits and 99.7 % data lies between 30 and 30 limits.

 

Chebyshevs Rule:  Chebyshevs rule give an approximation to how much data lies between ±10, ± 20 and ±35 limits. Even for non-normal distribution.

a.      What do you mean by Chebyshev’s rule?

Chebyshev’s Rule: Chebyshev’s theorem is a fact that applies to all possible data sets. It describes the minimum proportion of the measurements that lie must with in one, two or more standard deviations of the mean.

               Chebyshev’s inequality says that at least 1 – 1/K² of data from a sample must fall with in ‘k’ standard deviations from the mean. Here ‘k’ is any positive real number greater than one.

 

ð  K = the with in numbers / the standard deviation

And ‘k’ must be greater than 1.

It is used to find what present of the values will fall between given range of the numbers for a data set with given value of mean and standard deviation.