The following data was collected from 1 bag of Hershey Kisses®. Each Kiss® was weighed in grams with the wrapper and recorded in the table below. Hershey claims that there are 368 grams of chocolate in one bag. Hershey Kiss Weights in Grams 4.76 4.72 4.74 4.55 4.91 4.74 4.78 4.71 4.80 4.78 4.78 4.75 4.79 4.82 4.91 4.83 4.68 4.74 4.70 4.80 4.70 4.76 4.70 4.83 4.93 4.74 4.84 4.82 4.76 4.77 4.72 4.78 4.83 4.75 4.74 4.68 4.84 4.71 4.71 4.76 4.66 4.78 4.73 4.74 4.92 4.77 4.80 4.79 4.86 4.64 4.78 4.70 4.75 4.78 4.76 4.83 4.66 4.77 4.83 4.78 4.69 4.81 4.68 4.78 4.88 4.72 4.85 4.85 4.81 4.74 4.80 4.82 4.84 4.70 4.85 4.70 4.81 4.72 4.79 4.73 4.61 Standard Deviation & the Empirical Rule: Variation is a big factor in the analysis of most any data set and it will be very important to have a way of measuring it. Standard Deviation is one such measure. Find the Standard Deviation of the data. You can use the stdev or stdev.s functions in Excel. A bell-shaped distribution with a single peak is called a normal distribution. There is a rule for normal distributions that can help you have some feeling for what the standard deviation is telling you. It's called the Empirical Rule and is stated below: For any data set having a Normal distribution, the following are true: - Approximately 68% of the data values will be within one standard deviation of the mean. - Approximately 95% of the data values will be within two standard deviation of the mean. - Approximately 99.7% of the data values will be within three standard deviation of the mean. Use the mean (to the nearest thousandth), the standard deviation (to the nearest thousandth), and the Empirical Rule to find answers to the following: a) Find the percentage of all the Kisses in the bag that fell within 1 standard deviation of the mean? ... within 2?… within 3? (Show how you calculated these percentages!)
9. The following data was collected from 1 bag of Hershey Kisses®. Each Kiss® was weighed in grams with the wrapper and recorded in the table below. Hershey claims that there are 368 grams of chocolate in one bag.
| Hershey Kiss Weights in Grams | ||||||||
|---|---|---|---|---|---|---|---|---|
| 4.76 | 4.72 | 4.74 | 4.55 | 4.91 | 4.74 | 4.78 | 4.71 | 4.80 |
| 4.78 | 4.78 | 4.75 | 4.79 | 4.82 | 4.91 | 4.83 | 4.68 | 4.74 |
| 4.70 | 4.80 | 4.70 | 4.76 | 4.70 | 4.83 | 4.93 | 4.74 | 4.84 |
| 4.82 | 4.76 | 4.77 | 4.72 | 4.78 | 4.83 | 4.75 | 4.74 | 4.68 |
| 4.84 | 4.71 | 4.71 | 4.76 | 4.66 | 4.78 | 4.73 | 4.74 | 4.92 |
| 4.77 | 4.80 | 4.79 | 4.86 | 4.64 | 4.78 | 4.70 | 4.75 | 4.78 |
| 4.76 | 4.83 | 4.66 | 4.77 | 4.83 | 4.78 | 4.69 | 4.81 | 4.68 |
| 4.78 | 4.88 | 4.72 | 4.85 | 4.85 | 4.81 | 4.74 | 4.80 | 4.82 |
| 4.84 | 4.70 | 4.85 | 4.70 | 4.81 | 4.72 | 4.79 | 4.73 | 4.61 |
Standard Deviation & the
For any data set having a Normal distribution, the following are true:
- Approximately 68% of the data values will be within one standard deviation of the mean.
- Approximately 95% of the data values will be within two standard deviation of the mean.
- Approximately 99.7% of the data values will be within three standard deviation of the mean.
Use the mean (to the nearest thousandth), the standard deviation (to the nearest thousandth), and the Empirical Rule to find answers to the following:
a) Find the percentage of all the Kisses in the bag that fell within 1 standard deviation of the mean? ... within 2?… within 3? (Show how you calculated these percentages!)
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