Apply the statistical techniques (descriptive statistics) and completely describe your data set for both variables in the light of following questions: Each (X,Y) has 20 observations.

Question 1.

a. Discuss the types and level of measurement of the variables in the data.

b. Prove that A.M>G. M>H.M (For both the variables).

c. Estimate the values of Q3, D7 and P49 and Interpret the results.

d. Compare Relative Dispersions of X and Y. Using (i) Quartile Coefficient of Dispersion and (ii) Coefficient of Variation.

e. Explain whether the above two measures in part (d) provide the same information.

f. Which Variable is more consistent.

g. Discuss the shape of the variables X and Y using results of Mean, Median and Mode.

h. Obtain skewness by Karl Pearson's formula, For which variable (X,Y) skewness is more sharp.

i. Obtain the Bowley's coefficient of skewness. Is there any change in the decision regarding the shape of the variables?

j. Draw a scatter plot of the data.

k. Obtain Pearson's coefficient of Correlation and interpret the results.

l. Discuss what changes will there be on the value of the correlation coefficient if we transform variables X (first variable in the data) and Y (second variable in the data) using the following expressions. will there be any change in the value of rxy, if so then why or if not then why, please discuss.

u= 5x+46 and v=3y+2

Data Set: Diamond Prices

Data of 20 round-cut diamonds along with their prices are taken from a newspaper

X= Weight of diamonds in carat

Y = Price in Singapore dollars

X 0.3, 0.3, 0.3, 0.3, 0.31, 0.31, 0.31, 0.31, 0.31, 0.31, 0.32, 0.32, 0.33, 0.33, 0.34, 0.34, 0.34, 0.34, 0.34, 0.34

Y 1302, 1510, 1510, 1260, 1641, 1555, 1427, 1427, 1126, 1126, 1468, 1202, 1327, 1098, 1693, 1551, 1410, 1269, 1316, 1222

Apply the statistical techniques (descriptive statistics) and completely describe your data set for both variables in the light of following questions: Each (XX) has 20 observations. Question 1. a Discuss the types and level of measurement of the variables in the data. b. Prove that A.M>G. M3H.M (For both the variables). c. Estimate the values of Q3, D7 and P49 and Interpret the results. d. Compare Relative Dispersions of X and Y. Using (1) Quartile Coefcient of Dispersion and (ii) Coefficient of Variation e. Explain whether the above two measures in part (d) provide the same information. f. Which Variable is more consistent. g. Discuss the shape of the variables X and Y using results of Mean, Median and Mode. h. Obtain Mb)! Karl Pearson's formula, For which variable (XX) Wis more sharp. i. Obtain the W coefcient of m Is there any change in the decision regarding the shape of the variables? j. Draw a scatter plot of the data. k. Obtain Pearson' s coefcient of Correlation and interpret the results. 1. Discuss what changes will there be on the value of the correlation coefcient if we transform variables X (rst variable 1n the data) and Y (second variable in the data) using the following expressions. will there be any change in the value of rm.l if so then why or if not then why, please discuss. u= 5x+46 and v=3y+2 Data Set: Diamond Prices Data of 20 round-cut diamonds along with their prices are taken from a newspaper X: Weight of diamonds in carat Y = Price in Singapore dollars X 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0 0. 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 l l l l l l 2 2 3 3 4 4 4 4 4 4 Y 1 l l l l l l l l l l 1 l l l l l l 1 l 3 5 5 2 6 5 4 4 l l 4 2 3 0 6 5 4 2 3 2 0 l l 6 4 5 2 2 2 2 6 0 2 9 9 5 l 6 1 2 2 0 0 0 l 5 7 '1' 6 6 8 2 '3' 8 3 l 0 9 6 2