Week 2 workshop - Assignment Example

Answer A. Frequency Table The frequency table is a method of counting the number of occurrences of a particular value in a given data set. The table below shows the frequency table for the income of the corporate customers:SalaryCount10000012000002300000340000025000001B. Measure of Central TendencyIt is evident from the frequency table that the salary of corporate customers follows a normal curve. The same is shown with the help of a histogram:For a normal curve, the best measure of central tendency is the mean.

The mean is computed by summing the observations and dividing by the number of observations (Keller, 2012). There are no outliers here and the frequency graph is not skewed. Moreover, salary is generally a continuous variable. Hence mean (average) is the appropriate measure for measuring the central tendency. The average salary of the corporate customers is $300,000.C. Additional salary points of $500,000 and $600,000The frequency graph with addition of new salary points of $500,000 and $600,000 will affect the skewness of the frequency distribution.

The graph is now positively skewed from mean as shown in the diagram below:The appropriate measures of central tendency for skewed distribution are either mean or median. Median is a more appropriate measure for highly skewed distributions. The skewness of the graph that we have plotted is not very high. Hence the best measure of central tendency is the mean. The average salary of the corporate customers is now $345,455.Answer 2Gender is an example of nominal data. It can take either of the two values: Male or Female.

Mode which is the value which has the highest frequency in the given data set is the best measure of central tendency in this case (QuickMBA, 2010). The mode of the distribution will tell us whether the data has more males or more females which is an appropriate measure for central tendency.Answer 3The three key different measures of central tendency are Mean, Median and Mode. All the three are not the best measures for all types of distribution. They have different values for differently skewed distributions.

For a symmetrical distribution, all the three measures converge on the same value. Mean is the most sensitive measure to skewness (Levin and Rubin, 2009). In case the distribution contains outlier values which impact the skewness of the distribution positively or negatively, the mean moves from being the highest (positively skewed distribution) to being the lowest (negatively skewed distribution). In any distribution, median is always in the middle of mean and mode. Median is the least sensitive measure for skewed distributions.

Answer 4Standard deviation and variance are both the measures of dispersion. Standard deviation is the square root of variance. Variance is the average value of the squared difference of the each value and the mean. Since variance is calculated after squaring, all the differences take positive value. Moreover, larger differences get more weight and are more suitable in cases where there are more outliers. Standard deviation is of the same unit as the data. Variance of the sum or the difference of uncorrelated random variables is the sum of their variables which makes it useful.

ReferencesLevin, R.I., & Rubin, D.S. (2009). Statistics for Management, 7th ed. New Delhi: Pearson Education Inc. Keller, G. (2012). Statistics for Management and Economics, 9th ed. Mason: South-Western CENGAGE LearningQuickMBA. (2010). Central Tendency. [Online]. Retrieved from: http://www.quickmba.com/stats/centralten/