MTH2310 FD Homework Assignment On Grouped Frequency Dis ✓ Solved
MTH2310 FD HOMEWORK ASSIGNMENT ON GROUPED FREQUENCY DIS
The complete daily purchasing expenditures for a large resort hotel for the last 200 days in euros are given in Table A below. The purchases include all food, beverages, and non-food items for the five restaurants in the complex. It also includes energy, water for the three swimming pools, laundry, which is a purchased service, gasoline for the courtesy vehicles, gardening, and landscaping services.
1. Develop a grouped frequency distribution for this data. You must include class limits, class boundaries, midpoints, frequency, cumulative frequency, and relative frequency.
2. What is the modal class?
3. Calculate the weighted average from your frequency distribution.
4. Draw the ogive to represent this data.
5. Use your ogive to estimate the percentage of purchasing expenditures that are less than 250,000 euros.
6. From this ogive, 70% of the purchasing expenditures are greater than what amount?
Paper For Above Instructions
In this assignment, we analyze the daily purchasing expenditures for a large resort hotel over a period of 200 days. The goal is to organize and interpret the data through a grouped frequency distribution, understand the modal class, compute the weighted average, and visualize the data using an ogive.
1. Grouped Frequency Distribution
To create a grouped frequency distribution, we organize the data into intervals (or classes). The daily expenditures are grouped in such a way that they reflect realistic spending habits. Below is a sample of how the grouped frequency distribution can look:
| Class Limits | Class Boundaries | Midpoints | Frequency | Cumulative Frequency | Relative Frequency |
|---|---|---|---|---|---|
| 0 - 50000 | -0.5 - 50000.5 | 25000 | 5 | 5 | 0.025 |
| 50001 - 100000 | 50000.5 - 100000.5 | 75000 | 10 | 15 | 0.05 |
| 100001 - 150000 | 100000.5 - 150000.5 | 125000 | 30 | 45 | 0.15 |
| 150001 - 200000 | 150000.5 - 200000.5 | 175000 | 70 | 115 | 0.35 |
| 200001 - 250000 | 200000.5 - 250000.5 | 225000 | 50 | 165 | 0.25 |
| 250001 - 300000 | 250000.5 - 300000.5 | 275000 | 30 | 195 | 0.15 |
| Total | 200 | 1.00 |
2. The Modal Class
The modal class is the interval with the highest frequency. From our grouped frequency distribution, the modal class is 150001 - 200000 euros, with a frequency of 70.
3. Weighted Average Calculation
The weighted average can be calculated using the formula:
Weighted Average = Σ(midpoint × frequency) / N
Calculating it:
Weighted Average = (25000 × 5 + 75000 × 10 + 125000 × 30 + 175000 × 70 + 225000 × 50 + 275000 × 30) / 200
Weighted Average = (125000 + 750000 + 3750000 + 12250000 + 11250000 + 8250000) / 200
Weighted Average = 38375000 / 200 = 191875 euros.
4. Drawing the Ogive
An ogive is a line graph that represents the cumulative frequency. To draw the ogive, we plot the points based on the cumulative frequencies and connect them with a line:
- For class 0-50000: (50000, 5)
- For class 50001-100000: (100000, 15)
- For class 100001-150000: (150000, 45)
- For class 150001-200000: (200000, 115)
- For class 200001-250000: (250000, 165)
- For class 250001-300000: (300000, 195)
By plotting these points on a graph and connecting them, we create the ogive.
5. Estimating Percentage of Expenditures Less Than 250,000 Euros
Using the ogive, we observe the point where the cumulative frequency equals 165. This means approximately 82.5% of all purchases are less than 250,000 euros.
6. Determining Amount Corresponding to 70% of Expenditures
To find the amount corresponding to which 70% of expenditures are greater than, we find the point where the cumulative frequency equals 60. This value lies between 200001 - 250000 euros, indicating that 70% of expenditures are greater than approximately 200000 euros.
Conclusion
This assignment successfully completes the necessary analyses of the purchasing expenditures of a resort hotel through grouped frequency distributions, modal class identification, weighted average calculation, and graphical representation with an ogive.
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