Question

5 2271 53 25-14-15 9 | 4 | 7 | 75 697 c 56542326565335433272 5 1-5-5 C D-9196355181855875-6414 21 2 2 T S-67-7811 511116813 7527685766 p |3|3|3|3|3|3|3|3|3|3|3|3|3|3|3|3|3|3|3|3 23-2 8833 733 12-17 6 6 5 5 4432-14 17 15.

(b) Which measures of central tendency are preferred for each variable? Why? (Hint:Use frequency histogram)

(c) Find the sample variance, standard deviation, and range for each variable.

(d) Describe the logical population and sample for this study. (There can be different reasonable answers with respect to the population. The question is, what total set of measurements is this data set intended to represent?)

Answer 1

(b) Which measures of central tendency are preferred for each variable? Why? (Hint:Use frequency histogram)

Ans:

Histogram of Quality, pH, Total So2, Color Density, Color pH Total So2 6.0 4.5 3.0 1.5 0.0 12 13 14 15 16 17 18 19 3.5 3. 3.7 38 3.9 4.0 Color 0 50 100 150 200 250 300 Color Density 6.0 A: 4.5 3.6 2.4 3.0 1.2 1.5 y.か 0.0 0.0 8 10 12 2 3 4 5 6 7 8

The variables Quality and Color are preferred to be used the mean measures of central tendency because both the datasets have near to symmetric without outlier observations.

The variables pH, Total So2 and Color Density are preferred to use the median measures of central tendency because pH has negative skewness, and Total So2 and Color Density have outlier with positive skewness. Hence, the median is not influenced by the skewness as well as an outlier.

(c) Find the sample variance, standard deviation, and range for each variable.

Ans:

Variable	StDev	Variance	Range
Quality	1.998	3.992	7.7
pH	0.1291	0.0167	0.51
Total So2	61.2	3748.8	279
Color Density	2.548	6.494	9.25
Color	1.594	2.542	5.45

(d) Describe the logical population and sample for this study.

Ans: The logical population for these variables is normal whereas some of the samples do not show the normal characteristics.