Createa histogram for theSales/SqFtvariable and answer the following questions:

• Is the distribution symmetric? If not, what is the skew?
• Are there any outliers? If so, which one(s)?
• What is theSqFtarea of the outlier(s)? Is the outlier(s) smaller or larger than the average restaurant in the database? What can you conclude from this observation?
• What measure of central tendency is more appropriate to describeSales/SqFt? Why?

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AI answer & explanation

To create a histogram for the Sales/SqFt variable and analyze its distribution, you'll typically follow these steps:

Collect Data: First, ensure you have the Sales/SqFt data available. This should be a numerical dataset.

Create Histogram:

• Use a data visualization tool or software (like Python with libraries such as Matplotlib or Seaborn, or software like Excel) to plot a histogram.
• The histogram will show the frequency of Sales/SqFt within defined bins.

Analyze Distribution:

• Check if the shape of the histogram is symmetric or if it has any skewness.
• If the left side and right side of the histogram are mirror images around a central point, the distribution is symmetric.
• If one tail is longer or fatter than the other, it has skewness. A longer right tail indicates right skew (positive skew), while a longer left tail indicates left skew (negative skew).

Detect Outliers:

• Outliers can be detected using graphical methods (like boxplots) or statistical methods (IQR method or Z-scores).
• For the IQR method, calculate the interquartile range (IQR):
  • Q1 (25th percentile), Q3 (75th percentile)
  • IQR = Q3 - Q1
  • Outliers are typically defined as any points below Q1 - 1.5 * IQR or above Q3 + 1.5 * IQR.
• Identify which data points fall into the outlier category.

Outlier Analysis:

• Once the outlier(s) are identified, report their Sales/SqFt values and the corresponding SqFt area.
• Determine if these outlier values are smaller or larger than the average (mean) Sales/SqFt for the dataset.

Conclusion:

• Discuss what your findings suggest about the dataset. If outliers are significantly higher or lower than the mean, they might represent exceptional cases (like very successful or struggling restaurants).

Measure of Central Tendency:

• Consider which measure of central tendency (mean, median, or mode) will best represent the dataset.
• If the distribution is skewed or has outliers, the median may be more appropriate because it is less affected by extreme values compared to the mean.

Example Analysis (Hypothetical):

1. Histogram: Visually represents the frequency of Sales/SqFt data.
2. Distribution: Not symmetric, right skew (longer right tail).
3. Outliers: Identified as a Sales/SqFt = 300 (SqFt = 2,500).
4. Outlier Comparison: Average Sales/SqFt = 100; hence 300 is larger than the average.
5. Conclusion: The high outlier may represent exceptionally profitable restaurants, suggesting opportunities or market anomalies.
6. Central Tendency: Median (more robust against outliers) is more appropriate than mean in this case.

For a true analysis, you would need the actual data to follow this process accurately. Please provide the dataset or summary statistics if you need further specific analysis or example values.