quant

A study was conducted by the West Company for the purpose of gaining insight into the characteristics of its retail customers. The sample consists of 5 variables. A random sample of 263 customers were surveyed. A descriptive statistics analysis was performed over the Income and Region of the Country variables. Results are presented below.

If the Variable is Continuous :

Table 1

Numerical Summaries for the Income Variable

Figure 1

Distribution of Customer Annual Income

If the distribution is symmetric:

From Figure 1, the distribution of customer annual income appears to be near bell-shaped and this is further supported by the reported near zero skewness value. This suggests that the mean could serve as a representative typical value and measure of the center. From Table 1, it can be seen that the average customer income is slightly over $51,000 annually. Based on the Empirical Rule and the standard deviation reported in Table 1, approximately 68% of customers have annual incomes between $41,018 and $61, 475.

If the distribution is asymmetric: (Calculate the Q1 and Q3 quartiles ( in Excel) to obtain the upper and lower bound of the IQR. JASP can give this too you by checking the ‘Quartiles’ check box under the ‘Statistics’ drop down arrow)

From Figure 1, the distribution of customer annual income appears to be skewed right. This is further supported by the reported the positive skewness value of 1.64. The kurtosis value of 3.52 further confirms the existence of more data values within the tails of the distribution than would be expected if the distribution were symmetric. Hence there is likely the presence of outliers or customers with incomes that are far larger that the typical customer. Since the value of the mean is highly impacted by the presence of outliers, it’s likely that the median could better serve as a representative typical value and measure of the center. From Table 1, it can be seen that the median customer income is slightly over $51,000 annually. Quartile values reported in Table 1 suggest that the middle most 50% of customers have an annual income range between $25,000 and $38,000.

If the Variable is Categorical

Table 1

Frequency Distribution Table for the Region Variable

Figure 1

Count of Customers by Region of the Country

From Figure 1, it can be seen that the largest percentage of customers reside in the Southwest region of the country. In fact, from Table 1 it can be seen that 74% of customers reside in the Southwest. This suggests that customers are not near uniformly spread across the four regions served by the company .