| unit sales | observed frequency |
| 20 | 3 |
| 40 | 6 |
| 55 | 9 |
| 65 | 12 |
| 70 | 15 |
| 89 | 18 |
| 90 | 21 |
| 105 | 24 |
| 110 | 27 |
| 120 | 30 |
The topic chosen is social science, which refers to the behavior of human beings and their relationships with society. The data collected expresses the social science aspect of human interaction with products. The data shows how the customer frequency of visiting a business premise influences unit sales. The customers portray different behavior in the purchasing trends where more visits result in increased sales units. Additionally, the reduced frequency of buys reduces the number of unit sales.
The chart represents quantitative data collected from the sales department showing the times that a certain sales limit is reached. The limits have different frequencies of occurrences depending on the number of customers at the shop at a certain period. Therefore, the sales frequencies determine how many sales units the business will experience during a certain period.
Central tendency
Central tendency refers to the similarity of data or the reasonableness of a set of data.
| unit sales | |
| Mean | 76.4 |
| Standard Error | 10.1797184 |
| Median | 79.5 |
| Mode | #N/A |
| Standard Deviation | 32.19109608 |
| Sample Variance | 1036.266667 |
| Kurtosis | -0.737995376 |
| Skewness | -0.376607985 |
| Range | 100 |
| Minimum | 20 |
| Maximum | 120 |
| Sum | 764 |
| Count | 10 |
The above chart shows the descriptive analysis for the sale units. The data shows the mean for the sales, which is 76.4 meaning that most of the sales are either more or less than 74. Additionally, the sales deviate by 32.19 from the mean. The sales lack a mode, which means that no amount of units sold is constant or repetitive.
| Regression Statistics | |
| Multiple R | 0.988405388 |
| R Square | 0.976945211 |
| Adjusted R Square | 0.974063363 |
| Standard Error | 5.184329535 |
| Observations | 10 |
| ANOVA | |||||
| df | SS | MS | F | Significance F | |
| Regression | 1 | 9111.381818 | 9111.382 | 338.9995 | 7.79736E-08 |
| Residual | 8 | 215.0181818 | 26.87727 | ||
| Total | 9 | 9326.4 |
The regression analysis gives a prediction of the trends based on the changes in the predictor variables. The trend line equation helps to predict the future patterns of activities. The x variable is the predictor, which explains the future behavior of the y variable. Figure 18.6 is the constant or the y-intercept. The intercept gives the effect of other factors other than x that affect the y-variable. The R2 explains the relationship between the y variable and the other predictor variables in the equation. The equation has an R-value of 0.9, which is very close to one indicating a strong explanatory power. That the sales units are to a high extent affected by the frequencies of purchases. Moreover, the line of fit identifies the units that best represent the data, while the units outside the line are called outliers.
The prediction for the future is that the unit sales at frequency 35 will be 140 units. The linear equation enhances the confidence in the prediction since the y-intercept is constant. Therefore, any change in the predictor variable will give the correct change in addition the relationship between the y-variable and the other variables is strong.
Histogram
| bin | Frequency |
| 0-20 | 3 |
| 20-40 | 6 |
| 40-60 | 9 |
| 60-70 | 15 |
| 70-90 | 21 |
| 90-110 | 27 |
| 110-120 | 30 |
| More | 0 |
The histogram shows that most sales lie to the right meaning right skewness. The skewness to the right means that most of the sales units lie above the mean sales. Therefore, the business experiences fewer cases of sales falling below the set meaning for the sales. Additionally, the pattern shows that sales increase with the increase in the frequency of purchase.
Pie chart
The pie chart shows data in a circular format divided into slices depending on the proportion of each item. The pie chart represents the data with an inclusion of the unit sales and the percentage when compared to the total sales. The pie chart indicates that 120 represent the highest sale units, which is 16% of the total sales. Moreover, 20 sales units represent the least amounts, which is 3% of the total sales.
Mean of sample data
| unit sales | |
| Mean | 76.4 |
| Standard Error | 10.1797184 |
| Median | 79.5 |
| Mode | #N/A |
| Standard Deviation | 32.19109608 |
| Sample Variance | 1036.266667 |
| Kurtosis | -0.737995376 |
| Skewness | -0.376607985 |
| Range | 100 |
| Minimum | 20 |
| Maximum | 120 |
| Sum | 764 |
| Count | 10 |
The mean of the sample data is 76.4, which represents the reasonableness of the data around the figure. Therefore, most of the sales rotate around the figure meaning that the units are slightly less or more than 76.4.
