Suitability for Interpretation
In order to know if data is suitable for interpretation one must determine if the data has measurable significance. This means that the sample size is large enough to to extrapolate information. The data in this case is quantitative and this means that measuring central tendency is more accurate but also that there is less subjectivity or interpretation in the results. The size of the group is also large enough to show significance in testing.
Factors affecting the validity of the data.
The validity of the data could be affected by a number of factors such as inaccuracy- the wrong number of customers or inaccurate transposition of numbers. This is an error factor which can bias results by creating erroneous data. The other problem that could impact the validity of the data might be a bias in the collection process. This would take place in situations were the data was altered by the collector for some reason such as a manager trying to make numbers look better. If discrepancies in the data are not present such as skewed results one can safely assume that the data was collected properly.
Data Reliability Factors
The data appears reliable with three years having over 1400 guests annually. The collection methods come from sales so this would be an accurate form of data collection for this scenario. Sales are based on many factors such as times, seasons, and other customer oriented factors. In this instance, the data should reliably show the volumes of customers based on a predictable pattern.
Steps taken to arrive at validity & reliability conclusion
- Validity of statistical conclusion
- Internal validity
- External validity (Jaggia & Kelly, 2014)
- Is their sufficient data (guests)
- Was the correct system used to collect data (hand written or POS)
- If so how reliable was the tool at collecting the data
- Was the data complete year over year (not missing days) (Jaggia & Kelly, 2014)
|Littletown Café Data|
|Lunch + Dinner Guest Counts by Date|
|* Memorial Day|
In this testing a line chart was chosen do to the chronology of the data (Jaggia & Kelly, 2014). There are trends in the data which are reflected over a specific period of time and in a chronology. This type of chart reveals the slowest and busiest days over the past three years. As well, this chart also shows the standard deviation for the days that might be most volatile with regard to guest volume. Using this form of line chart, decisions can be made as to how and when to allocate human resources based on the trends and patterns in the data.
Central Tendency & Variability
Step for Mean- The mean was found by adding all of the guests from each day which totals 3 years on 19 different days. The mean is then calculated by dividing by three (Jaggia & Kelly, 2014).
Step for Median- The median was calculated by arranging the guest data in ascending order- the smallest to the largest. The third number of the data set or (middle number) was used and this equals the median (Jaggia & Kelly, 2014).
Step for Mode- The mode was found by analyzing the number of guests to see which number repeated the most. The number repeating the most was the mode (Jaggia & Kelly, 2014).
Step for Standard Deviation- The standard deviation was found by subtracting the mean from each data point and squaring the result. The squared results were then were then calculated for their mean and the multiplied the mean by 1/n or (1/3). This provided the standard deviation (Jaggia & Kelly, 2014).
Measures of Central Tendency & Variability
The measure of the central tendency shows that there was little variance across the the last three years. There is an expected predictability in the data which shows that this data can be used with reasonable expectations of creating accurate schedules. The data also provided that certain days are busier than others which shows a detailed view of the labor requirements. Allocation of labor should be based on those days which are busiest and require the most labor.
Jaggia, S., & Kelly, A. (2014). ESSENTIALS OF BUSINESS STATISTICS: COMMUNICATING WITH NUMBERS. New York, NY: McGraw-Hill/Irwin.