Summary Statistics
1. **Problem statement:** Calculate and interpret the summary statistics for two outlets based on the provided data in part (b).
2. **Arithmetic mean ($\bar{x}$):** Sum all data points for each outlet and divide by the number of data points:
$$\bar{x} = \frac{\sum x_i}{n}$$
The mean represents the average value.
3. **Coefficient of Variation (CV):** This measures relative variability as a percentage:
$$\text{CV} = \frac{\text{standard deviation }(s)}{\text{mean }(\bar{x})} \times 100\%$$
It shows variability relative to the mean.
4. **Mode:** The value that appears most frequently in the dataset.
5. **Median:** The middle value when all data points are sorted in ascending order. If even number of observations, average the two middle values.
6. **Geometric Mean (GM):** The nth root of the product of n values:
$$\text{GM} = \sqrt[n]{x_1 \times x_2 \times \cdots \times x_n} = \exp\left(\frac{1}{n} \sum_{i=1}^n \ln x_i\right)$$
Useful for data measured in ratios or rates.
7. **1st and 3rd Quartiles (Q1 and Q3):** Q1 is the 25th percentile and Q3 is the 75th percentile. Sort data and find values at these percentiles.
8. **Pearson’s 1st coefficient of Skewness (SK1):** Measures asymmetry:
$$\text{SK1} = \frac{\bar{x} - \text{mode}}{s}$$
Positive SK1 means right-skewed, negative means left-skewed.
**Interpretation:**
- Mean gives central tendency.
- CV shows relative spread.
- Mode indicates the most common value.
- Median shows middle value unaffected by outliers.
- Geometric mean better for proportional data.
- Quartiles describe spread and identify outliers.
- Skewness tells about distribution symmetry.
Final answer depends on data from part (b). Replace $x_i$, $n$, $s$, mode, and data with actual values to complete calculations.