Question: Data was collected on the cost ($) for each cookie in a group of eight (8) yummy gourmet cookies. The data points and descriptive statistics
Data was collected on the cost ($) for each cookie in a group of eight (8) yummy gourmet cookies. The data points and descriptive statistics from an Excel statistical application are shown below. (The far left column contains the data points; the far right column reports the corresponding Z scores. The middle columns show common descriptive statistics.)
- After Jasmine viewed this data, she said "This data is very symmetrical: the mean and median are virtually the same value." Clearly state why you do or why you don't agree with Jasmine's statement.
- Jasmine continues... "I'm a little confused though. Since a symmetrical data set should follow the empirical rule, why doesn't the mean of $0.85 divided by the standard deviation of $0.13 equal an exact 3?" Clearly state a thorough answer to Jasmine's question.
| Cost per Gourmet Cookie $ (n = 8) | Statistics | Descriptive Statistics | Gourmet Cookie Cost ($) | Z Score |
|---|---|---|---|---|
| 1.00 | Mean | $0.8525 | 1.00 | 1.1581 |
| 0.94 | Standard Error | $0.0450 | 0.94 | 0.6870 |
| 0.87 | Median | $0.8750 | 0.87 | 0.1374 |
| 0.88 | Mode | $#N/A | 0.88 | 0.2159 |
| 0.74 | Standard Deviation | $0.1274 | 0.74 | -0.8833 |
| 0.65 | Sample Variance | $^2 0.0162 | 0.65 | -1.5899 |
| 0.75 | Kurtosis | -1.1968 | 0.75 | -0.8048 |
| 0.99 | Skewness | -0.3964 | 0.99 | 1.0796 |
| Range | $0.35 | |||
| Minimum | $0.65 | |||
| Maximum | $1 | |||
| Sum | $6.82 | |||
| Count | 8 | |||
| Coefficient of Variation = 14.94% |
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