The following data represents test scores: 55.35, 78.3, 22.9, 50.65, 67.5, 63, 46.1, 59.7, 57.45, 41.55, 108.25, 56.65, 50.75, 52.6, 35.2 Calculate the coefficient of kurtosis using the software method

The coefficient of kurtosis, using the software method, can be calculated as follows:

### Formula for kurtosis:
\[
K = \frac{n \cdot (n+1)}{(n-1)(n-2)(n-3)} \sum \left( \frac{(x_i - \mu)^4}{\sigma^4} \right) - \frac{3(n-1)^2}{(n-2)(n-3)}
\]
Where:
- \( K \) is the kurtosis.
- \( n \) is the number of data points.
- \( x_i \) is each data point.
- \( \mu \) is the mean of the data.
- \( \sigma \) is the standard deviation of the data.

Let's go step by step to calculate the kurtosis of the given data set.

The data set is:
\[ 55.35, 78.3, 22.9, 50.65, 67.5, 63, 46.1, 59.7, 57.45, 41.55, 108.25, 56.65, 50.75, 52.6, 35.2 \]

We will compute the following:
1. Mean \(\mu\)
2. Standard deviation \(\sigma\)
3. Kurtosis using the formula

I'll now calculate it.The coefficient of kurtosis for the given data set is approximately 4.08 using the software method.

Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:
1. How does kurtosis help in understanding data distribution?
2. What is the difference between positive and negative kurtosis?
3. How is kurtosis related to skewness in data analysis?
4. How does the software method of calculating kurtosis differ from the "classical" method?
5. Can kurtosis be used to assess the risk in financial data analysis?

**Tip:** High kurtosis indicates a distribution with heavier tails and sharper peaks, while low kurtosis reflects a flatter distribution.

Learn how to calculate the coefficient of kurtosis for a given data set using the software method. This solution involves descriptive statistics concepts like mean, standard deviation, and kurtosis. The data set includes scores such as 55.35, 78.3, and 108.25. Suitable for advanced high school or college students.

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