Pie chart Figure 1: Proportion of airline boarding in the US market. Figure 2: Bar graph showing airline boarding of top seven airlines in the US.

Descriptive Statistics

Table 1.

 Summary Statistics Metric Value Mean 3.6133 Standard Error 0.4965 Median 2.9800 Mode #N/A Standard Deviation 1.9231 Sample Variance 3.6983 Kurtosis 3.5831 Skewness 1.7839 Range 7.2700 Minimum 1.6800 Maximum 8.9500 Sum 54.2000 Count 15.0000 Confidence Level (95.0%) 1.0650

Meaning of each of the metric in the summary table

Table 2.

 Definitions of Metrics. Metrics Definition Mean Measures an average value of a given data Standard Error Measures variation of an estimated mean in a population Median The middle value of an ordinal data or ordered list Mode A value with the highest frequency in a distribution Standard Deviation Measures the degree of dispersion of data around a mean Sample Variance Magnified dispersion of data around mean by squaring standard deviation Kurtosis Measures lightness or heaviness of tails of a distribution relative to the normal distribution Skewness Measures the degree of asymmetry of a certain distribution relative to the normal distribution Range Measures dispersion of distribution based on the highest and the lowest data points Minimum The lowest value of a distribution Maximum The highest value of a distribution Sum The total of values in a distribution Count The number of data points in a distribution Confidence Level (95.0%) The probability of getting a valid value in a distribution (Carlberg, 2014)

According to Carlberg (2014), descriptive statistics comprise measures of central tendency and dispersion. Measures of central tendency show that the leading states (N = 15) in mineral production have a mean of \$3.61 billion and a median of \$2.98 billion. The apparent difference in the mean and the mode implies that the distribution of data is asymmetrical. Regarding the measures of dispersion, descriptive statistics indicate that mineral production has a standard error of 0.497, a standard deviation of 1.923, a variance of 3.698, a range of 7.27, a maximum 1.68, and a maximum 8.95. Although the standard error indicates that the estimated mean is accurate for it deviates slightly from the population mean (M = 3.613, SE = 0.497), the standard deviation, variance, and range depict that the distribution of data points is highly variable. The distribution has profoundly positive kurtosis (3.558), which shows peaky distribution, and a slightly positive skewness (1.78), which indicates asymmetrical distribution. Since 95% confidence interval is 1.07, it indicates that the valid mean of the population falls between \$2.54 and \$4.68 billion. The examination of data shows the existence of outliers \$8.95 billion for Arizona and \$6.48 billion for Nevada are extreme values in the distribution.

Histogram Figure 3: Histogram showing weekly distribution of bar soaps per five million bins.

Brief analysis of the chart

Histogram presents important information required in the production and sale of bar soaps. Jani (2014) explains that histogram allows visualization and conversion of numerical data into categories called bin. The analysis of weekly sales in millions for a year shows that Procter and Gamble registered the highest sales of between 20 to 25 million bar soaps in 19 weeks out of 52 weeks. In 14/52 weeks, Procter and Gamble recorded the second highest sales ranging between 10 to 15 million bar soaps in 14/52 weeks. Sales between 15 and 20 and 25 and 30 million bar soaps had the same frequency as each occurred in 8 weeks. Sales of between 30 and 35 million occurred in 2 weeks, whereas sales of between 35 and 40 million bar soaps happened in a week. Regarding distribution, the sales have a positive skew as most sales are below the average. Therefore, the histogram implies that the management should limit the number of bar soaps to be between 10 and 30 million in most weeks (49). Similarly, salespeople ought to understand that the trend of sales varies from 15 to 30 million bar soaps with dominance in 19 weeks followed by 14 and 16 weeks.

Carlberg, C. G. (2014). Statistical analysis: Microsoft Excel 2013. Indianapolis, IN: Que.

Jani, P. N. (2014). Business statistics: Theory and applications. New York, NY: PHI Learning.