Question

[4 5 5 2 4 4 6 3 3 7 5 3 6 3 4 4 6 5 4 5 3 7 5 5 4 2 6 5 6 6] This is my dataset Find mean, median, mode, variance, standard deviation, coefficient of variation, range, 70th percentile, 3rdquartile of the data and skewness and define what each of these statistics measure. For example, mean is a measure of the central tendency, what about the rest? Use Chebyshev’s rule to find the percent of data values which are located in 1,5 standard deviations of the mean; Create a new series by standardization. It means find z-score for each datavalue in the dataset. Find out if there is any outlier using z-score rule. If you forgot that check 21st slide of lecture note 3b; Draw Box plot (5-number summary of the data) and find if there are any outliers;

Answer 1

Solution :

Mean, Median and Mode are the measures of central tendency.

Mean measure the average of data values. Median is the value that separates bottom 50% observations form that of top 50% observations. Mode is most repeating observation in the given data.

Variance, standard deviation, coefficient of variation and the range are the measures of dispersion.

Variance and standard deviation measures the spread of all the observations from it's mean. Coefficient of variation is the ratio of standard deviation to th mean. The higher the CV, the greater is the level of dispersion from it's mean.

The Chebychev's rule applies to all types of data sets and it states that, the minimum proportion of observation that lies within "k" standard deviations from the mean is this is true for ( k > 1).

For k=5, we get; . And hence the proportion of observation that lie within 5 standard deviation from the mean of data is, 0.96.

Consider the following output;

The column "standardized" gives the standardized values ( or Z scores ) for the data. Since there is not any observation whose Z score lie outside the the interval (-2, 2) we conclude that there is no outlier in the data.