The amounts shown here are the fees charged by Quik Delivery for the 40 small packages it
The given data consists of 40 fee amounts charged by Quik Delivery for delivering small packages. The task involves constructing a stem-and-leaf display to visualize the distribution and then interpreting the distribution based on this display. The first step is to organize the data into a stem-and-leaf plot, which provides a clear representation of the frequency of fee amounts in different ranges. Subsequently, analyzing the display allows us to understand the shape, spread, and central tendency of the data, revealing insights about the delivery fee pattern during the specified period.
Paper For Above instruction
Constructing a stem-and-leaf diagram from the provided delivery fee data is a fundamental step in descriptive statistics, offering a visual summary that highlights the distribution and variability of the dataset. The data set comprises the following 40 fee amounts:
4.03, 3.56, 3.10, 6.04, 5.62, 3.16, 2.93, 3.82, 4.30, 3.86, 4.57, 3.59, 4.57, 6.16, 2.88, 5.03, 5.46, 3.87, 6.81, 4.91, 3.62, 3.62, 3.80, 3.70, 4.15, 2.07, 3.77, 5.77, 7.86, 4.63, 4.81, 2.86, 5.02, 5.24, 4.02, 5.44, 4.65, 3.89, 4.00, 2.99
To construct the stem-and-leaf plot, first identify the range of the data. The smallest value is approximately 2.07, and the largest is 7.86. The stems will represent the units digit of the dollar amount, and the leaves will represent the decimal part, scaled appropriately. Typically, for financial data with cents, we round or convert to integers for simplicity.
In this case, the stems will be the whole dollar amounts 2, 3, 4, 5, 6, 7 and the leaves will be the cents rounded to the nearest whole number. For example, 4.03 becomes stem 4, leaf 03; 3.56 becomes stem 3, leaf 56; and so forth.
Organizing the data, the stem-and-leaf display is:
2 | 07 88 86 86 99
3 | 10 16 59 62 62 70 77 82 86 87 89
4 | 02 15 30 57 57 63 65 81 91
5 | 02 03 24 44 46 54 62 77
6 | 04 16 81
This plot shows that most of the delivery fees are clustered between $3.00 and $5.50, with a few higher fees reaching above $6.00 and one outlier at $7.86. The distribution appears to be somewhat right-skewed, with a tail extending towards higher fees, indicating that while most deliveries cost around $3 to $5.50, there are some instances with significantly higher fees.
In terms of spread, the data is relatively concentrated in the lower ranges but has a few values spread across higher fee points. The presence of outliers or high-value fees indicates variability in delivery charges, possibly due to factors such as distance or priority service.
Interpreting this distribution provides insights into the typical cost of delivery services, revealing that most fees fall within a predictable range, but occasionally, higher charges occur. This analysis can help business managers understand fee variability, set appropriate pricing strategies, and forecast revenue more effectively.
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