Question

Using the data from Data Set VII in Appendix B, find the mean, median, mode, range, variance, and standard deviation of the acreage owned by the municipalities. Comment on the skewness of the data, using the Pearson coefficient of skewness.

 

Data from in Set VII Appendix B

Answer 1

The acreage owned by 35 municipalities in south western in increasing order is as follows:

10, 22, 38, 44, 48, 58, 60, 62, 70, 78, 87, 100, 105, 120, 130, 150, 160, 165, 180, 198, 200, 200, 218, 223, 227, 234, 250, 306, 340, 384, 402, 600, 1200, 3700, 4200

 

Mean, X̅ = ΣX/n

               = 14569/35

               = 416.26

               = 416. 3 when rounded.

 

The data set has an odd number of values; hence, the median is the middle value.

 

Median = 18th value from the data set in increasing order = 165

 

Since 200 occurred 2 times – a frequency larger than any other number – the mode for the data set is 200

Mode = 200 (frequency = 2)

Range = Highest value – Lowest value

            = 4200 – 10

            = 4190

 

Sum of the squares of the given data set is,

Variance, s2 = [ΣX2 – {(ΣX)2/n}]/(n – 1)

                      = {(34229217 – (14569)2/35}/34

                      = (34229217 – 6064450.3)/34

                      = 828375.5

 

The standard deviation for the given data set is

Standard deviation, s= √variance

                                      = √828375.5

                                     = 910.2

 

Pearson coefficient of skew ness is as follows:

Skewness = 3(X̅ - MD)/s

                   = (3(416.3 – 165)/910.2

                   = 0.83

Since the Pearson coefficient of skew ness is positive, the distribution is positively skewed.

Since the Pearson coefficient of skew ness is positive, the distribution is positively skewed.