Question

. Choose a data set with 10-30 data values. (This could include but Is not limited to the closing price of a stock for 10-20 days, 10-20 of your exam grades, etc) You must all choose a different data set!! Compute the mean, median, mode, quartiles, IQR, SIQR, variance and standard deviation. Then report the relative position (from the median in terms of amount of SIQRs and also from the mean in terms of amount of standard dev's) of both the highest and lowest data values.

Answer 1

We take number of COVID-19 cases in different countries (as reported on 3:00 AM GMT, 20-04-2020) as follows.

Country	No of cases	Country	No of cases	Country	No of cases
USA	764265	China	82747	Switzerland	27740
Spain	198674	Iran	82211	Portugal	20206
Italy	178972	Russia	42853	India	17615
France	152894	Brazil	38496	Peru	15628
Germany	145742	Belgium	38496	Ireland	15251
UK	120067	Canada	35056	Austria	14749
Turkey	86306	Netherlands	32655	Sweden	14385

Suppose, random variable X denotes the number of COVID-19 cases in different countries.

In our data, number of countries observed

Mean-

Mean is given by

Median-

Arranging the given data in increasing order we get as follows.

14385,    14749,    15251,    15628,    17615,    20206,    27740,

32655,    35056,    38496,    38496,    42853,    82211,    82747,

86306, 120067, 145742, 152894, 178972, 198674, 764265.

There are 21 values.

So, median is (21+1)/2 th i.e. 11 th value.

Hence, median is 38496.

Mode-

We observe that 38496 occurs for highest (twice) number of times.

Hence, mode is 38496.

Quartiles-

Second quartile (also known as median) is the (21+1)/2 th i.e. 6 th value.

Hence, second quartile is 38496.

This data separates the whole data set into two equal parts.

First quartile is the (11+1)/2 th i.e. 6 th value.

Hence, first quartile is 20206.

Third quartile is the (11-1)+(11+1)/2 th i.e. 16 th value.

Hence, third quartile is 120067.

IQR-

Inter quartile range = 120067 - 20206 = 99861

SIQR-

Semi-inter quartile range = (120067 - 20206) / 2 = 49930.5

Variance-

Variance is given by

Standard deviation-

Standard deviation is given by

Relative position-

Highest - Median = 764265 - 38496 = 725769 = 14.53558 * SIQR

Median - Lowest = 38496 - 14385 = 24111 = 0.4828912 * SIQR

Highest - Mean = 764265 - 101190.9 = 663074.1 = 13.27994 * SIQR

Mean - Lowest = 101190.9 - 14385 = 86805.9 = 1.738535 * SIQR