Here is my work:
The tuckshop at Narangba Valley State High School is a profitable business that offers a large variety of food and beverage options to students of a lunch time. The school has been collecting and collating data based on student’s purchases and are keen to determine which product is ‘the best’ product to market to new students.
Formulate - Define what is meant by ‘is best’?
My definition of ‘the best’ is what is best for the students and what they like the most out of their ratings, and the amount of profit the foods make each month and year. I am going to be deciding what is the best by making graphs, calculation and using mean, median and mode.
I will be using these things as graphs, will show me how much and the difference between items liked by students, and other things such as mean, median, mode, range, and outliers, will help me make comparisons and draw conclusions.
Solve - Select and compare a minimum of two products and show the data that will be used
I have chosen to compare this on what the students like the most, and how much profit the school will earn as it can show what the students like the most so that the students will like it and enjoy and like it the most.
Statistical Analysis of chosen products
Using your data sets what stats will you calculate?
Manual Calculation: Data Set 1
Measure Calculations
Mean Breaka-3.8+4+4.2+3.6+4.7+4.9+4.8+4.7+4.9+5+5+3.5+3.1+4.6+3.7=64.5÷15=4.3
Burgers-3.04
Median Breaka-3.1,3.5,3.6,3.7,3.8,4,4.2,4.6,4.7,4.7,4.8,4.9,4.9,5,5=4.6
Burgers-3
Mode Breaka-3.1, 3.5, 3.6, 3.7, 3.8, 4, 4.2, 4.6, 4.7, 4.7, 4.8, 4.9, 4.9, 5, 5=4.7
Burgers-3.9
Range Breaka-3.1, 3.5, 3.6, 3.7, 3.8, 4, 4.2, 4.6, 4.7, 4.7, 4.8, 4.9, 4.9, 5, 5=1.9
Burgers-2.6
Excel Calculations: Data Set 2
Measure Calculations
Mean Breaka-$202
Burger-$208
Median Breaka-$186
Burger-$216
Mode Breaka-Non-Modal
Burger-Non-Modal
Range Breaka-$361
Burger-$198
Data Displays
Hand draw or use technology (excel) to generate data displays below.
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Interpretation of Data (Data analysis)
Answer the following questions below:
• Is there a shape to your data (distribution)? What is it?
Yes, there sort of is. For example, it is sort of symmetrical and has no skewness, and the range of profit is large, which indicates that there are high and low values in the distribution.
• Explain what this means.
In mathematics and statistics, distribution refers to the way in which the values of a variable are spread out or arranged, such as in a normal distribution or a skewed distribution.
• Are there any outliers in the data?
The range of profit is $361, which is quite large compared to the mean and median.
• What are the outliers?
$361 ?
• What impact do outliers have on the data?
They could do the following:
- The mean would be affected and may no longer accurately reflect central tendency.
- The range would be inflated and may not accurately reflect the spread of the majority of the data.
- Depending on the location of the outlier, the median could be affected and may not accurately reflect central tendency either.
- The shape of the distribution could be affected, potentially causing the data to appear more skewed than it actually is.
- Outliers could also affect any subsequent data analyses, such as regression and forecasting, by creating inaccuracy in the predictions.
• Use calculations to demonstrate this impact. (By comparing data)
BREAKA
Student Ratings With Outlier
Mean Median Mode Range
4.3 4.6 4.7 1.9
BREAKA
Student Ratings Without Outlier
Mean Median Mode Range
Even Spread Even Spread Even Spread Even Spread
BURGER
Student Ratings With Outlier
Mean Median Mode Range
3.04 3 3.9 2.6
BURGER
Student Ratings Without Outlier
Mean Median Mode Range
2.92 2.9 3.9 1.9
BREAKA
Profit With Outlier
Mean Median Mode Range
202 186 Non-Modal 361
BREAKA
Profit Without Outlier
Mean Median Mode Range
191.14 181.5 Non-Modal 129
BURGER
Profit With Outlier
Mean Median Mode Range
208 216 Non-Modal 198
BURGER
Profit Without Outlier
Mean Median Mode Range
219.07 219.5 Non-Modal 65
All of the above is the infomation and nothing is to be changed, but using that info answer this :
Decision Making
You are now required to make your decision about which one is the best:
• Which central tendency have you chosen to make your decision?
• Why would this be used?
• What evidence supports this choice?
Write your decision in sentence format.
Decision Making:
• Which central tendency have you chosen to make your decision?
I have chosen to use both mean and median to make my decision.
• Why would this be used?
I have chosen to use both mean and median because the mean is good for determining the overall average, while the median is good for determining the central value that is not impacted by outliers.
• What evidence supports this choice?
The evidence that supports this choice is that the mean and median for each product are relatively close, indicating that there are no significant outliers impacting the data.
Write your decision in sentence format:
Based on the data collected, I have determined that both 'Breaka' and 'Burgers' are good products to market to new students, as they have similar mean and median values for both student ratings and profits.
Is your choice of which product is the most reasonable, based on the analysis you have completed and the data you were provided? Why/why not?
As an AI language model, I do not have the specific data or analysis that was conducted. However, based on the analysis presented in the report, the choice of which product is best seems reasonable. The analysis included various statistical measures, such as mean, median, mode, range, and the use of graphs to compare products. The decision-making process involved considering which central tendency to use for the analysis and how outliers might impact the data. Therefore, based on the rigor and thoroughness of the analysis, it seems that the choice of which product is the best is reasonable.
The following needs to be included as a summary: The aim of the report, how you defined what is best, which data you used, what decision you made in the end after analysing the data and if your answer is reasonable.
Can you please write the summary including:
The aim of the report, how you defined what is best, which data you used, what decision you made in the end after analysing the data and if your answer is reasonable.
The aim of this report was to determine the "best" product to market to new students of Narangba Valley State High School's tuckshop based on student preferences and profitability. In order to define what is best, a combination of student ratings and profit figures were used. Data sets were collected and analysed including measures such as mean, median, mode, range, and the use of graphs to compare products. Both "Breaka" and "Burgers" were found to be good products to market to new students, based on their similar mean and median values for both student ratings and profits. Overall, the answer is reasonable given the rigor and thoroughness of the statistical analysis presented in the report.
To make the decision about which product is the best, I have chosen to use the mean as the central tendency. This is because the mean takes into account all the data points and provides an average value, which can be a good representation of the overall student preference and profitability.
The evidence that supports this choice is that the mean value gives us an idea of the average student rating and average profitability for each product. It takes into account both high and low values in the dataset and provides a balanced measure of central tendency.
Based on the mean values calculated, the data shows that "BREAKA" has a higher mean student rating of 4.3 compared to "BURGER" which has a mean rating of 3.04. This suggests that, on average, students prefer "BREAKA" over "BURGER". Additionally, the mean profit for "BREAKA" is $191.14 compared to $219.07 for "BURGER". This indicates that "BURGER" is more profitable than "BREAKA" on average.
Therefore, based on the mean student ratings and profitability, my decision is that "BURGER" is the best product to market to new students at Narangba Valley State High School.