The sixth decile ( D6) of 5, 3, 2, 6, 8, 4 is:
5.20
The correct answer is 5.2.
Key Points
- Deciles divide a set of data into ten equal parts.
- The n-th decile separates the lowest (10n - 90)% of the data from the highest (90 - 10n)% of the data.
- To calculate the decile, the data must be ordered and the formula \(Dn = X[(n/10) * (N+1)]\) should be used.
- If the result is not a whole number, interpolation should be used to estimate the decile value.
- Deciles are often used in statistics to summarize a data set and identify values that separate the data into different percentiles.
- A decile is just one type of quantile. Other measures, such as quartiles and percentiles, can also be calculated.
- The value of a decile can be affected by outliers and extreme values in the data set. It is important to identify and handle outliers before calculating deciles to ensure accurate results.
Additional Information
- A decile is a set of quantiles that divides a data set into ten equal parts.
- The sixth decile (D6) is the value that separates the lowest 60% of the data from the highest 40% of the data.
- In other words, 60% of the data values are below D6 and 40% of the data values are above D6.
- To calculate the sixth decile for a given data set, we first need to order the data in ascending order: 2, 3, 4, 5, 6, 8.
- The formula for calculating the decile is as follows:
- \(Dn = X[(n/10) * (N+1)]\), where X is the sorted data set, n is the decile (in this case, 6), and N is the number of data points (in this case, 6).
- \(D6 = X[(6/10) * (6+1)] = X[(6/10) * 7] = X[4.2]\)
- Since 4.2 is not a whole number, we use interpolation to estimate the sixth decile:
- \(D6 = (X[4] + X[5]) / 2 = (5 + 6) / 2 = 5.2\)
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