1. Mean, Median, Mode
The Mean is the simple average of the data values. Most appropriate for symmetric data.
The Median is the middle value. It’s best for skewed data.
The mode is the value that occurs the most often.

2. Symmetric Data
The mean works best with this kind of data. It’s the best estimator of the center of the data.

3. Skewed Data
Because the extreme values pull the mean toward them, the median is the most appropriate measure of central tendency for skewed data.

4. Our data: No. of Bags
This data is fairly symmetric. The sample average and sample variance are the most appropriate.

5. Our data: Truck Age
This data appears to be slightly skewed left. The best measure of central tendency is the median, and of the variability is the range and percentiles.

6. Our data: Truck Weight
This data appears to be slightly skewed left. The best measure of central tendency is the median, and of the variability is the range and percentiles. Because of the low extreme values, the sample average would be lower than the sample median.

7. Variance vs. Standard Deviation
The variance is simply the square of the standard deviation:

8. Which one to use?
Variance is used in many statistical analysis techniques.
But standard deviation is more interpretable because its units are the same as the units of the observations.

9. Central Tendency and Variability
Measures of central tendency give us a good point estimate of the population mean.
Measures of variability help us to understand how much those estimates tend to vary across multiple samples.

10. Central Tendency and Variability
Combined these two measures can be used to create confidence intervals, a combination of margins of error with sample averages.
Also, they can be used in conjunction to perform hypothesis testing in order to determine if a given hypothesis is refuted by data.

11. Our data: Numerical Summary