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The sale data involves two discrete variables, sales per customer and number of customers which take a finite set of values. Standard deviation measures the spread of observation or variation of the observation from the mean. It also measures how well the data is represented by the mean. A high standard deviation indicates the observations are spread over a large range while a low standard deviation indicates observations are clustered close to the mean. If the standard deviation is large it means the mean is not a good representation of the observed data set. Sales per customer mean is $10.5 and standard deviation $5.916; several customers mean is 29.1 and standard deviation 21.844 (McManus, 2001, p. 1). There is a large deviation in the sale per customer according to the calculation while the deviation in the customer number is small.
Variance measures volatility or dispersion of how far are the observations from the expected mean, it is calculated from the mean as average squared deviation and is always positive. Large values of the variance denote large dispersions, which implies the mean of the data set is not a good representation of the observed data. Sale per customer has a moderate dispersion of 35 while customer number shows large dispersion of 477.147 (Bennett, 2006, p. 59).
The minimum value denotes the least or the smallest value in the observations of the data set. The minimum values for the sale per customer and number of customers are $1 and 1 respectively. Maximum value denotes the largest value in the observations of the data set. The maximum values for the sale per customer, and the number of customers is $20and 75 respectively. The two extreme values of the maximum and minimum are crucial in calculating the range of the observations since the range is their difference between the two statistics. (Bennett, 2006, p. 91).
The range is used to measure the variation of the observations in a data set. It is the difference between the maximum and the minimum value in the observations. Larger values of the range indicate high variation while small value indicates minimal variation. A sale per customer range is $19 while that of several customers is 74 (Trochim, 2006, p. 1).
Summary of the Descriptive Statistics of Sales Data
The distribution of the data from the calculation of descriptive statistics can only be approximated. Assuming the observation data meet the assumptions of the central limit theorem, we can approximate the distribution of the data set. Since the sum of the variables observed has a finite variance, we can conclude the data is approximately normally distributed. From the descriptive statistics, it is hard to comment on the distribution conclusively without plotting the graphs for the data set. Distribution entails how the observations are dispersed on both sides of the mean, the right and left sides.
Clearly, from the histogram graph, it is easier to observe that data is not evenly distributed about the mean, it is slightly skewed to the right. It also shows there is moderate dispersion from the mean on the numbers of customers.
Clearly, from the histogram graph, it is easier to observe that data is evenly distributed about the mean. It also shows there is even dispersion from the mean of sale per customer. The observed data can therefore be taken to be approximately normal.
Reference List
Bennett, B. (2006). Statistical reasoning for everyday life. New York. McMillan Publishers.
McManus, A. (2001). Descriptive analysis. Web.
Trochim, W. (2006). Descriptive statistics. Web.
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