deciles
points that divide the frequency distribution into equal tenths.
Deciles are statistical values that divide a set of observations or data into ten equal parts; each part represents 10% of the data. Deciles are commonly used in descriptive statistics to analyze the distribution of a dataset and to find key measures such as the median, quartiles, and percentiles.
To calculate the deciles of a dataset, the data must first be sorted in ascending or descending order. Then, the position of each decile is calculated using the following formula:
Position of decile = (n + 1) * k/10
where n is the total number of observations in the dataset and k varies from 1 to 9 to calculate the 1st, 2nd, 3rd, …, 9th deciles.
For example, if there are 50 observations in a dataset, the position of the 5th decile would be:
(50 + 1) * 5/10 = 5.5
This means that the 5th decile is between the 5th and 6th observations in the sorted dataset.
Once the position of each decile is calculated, the values of the dataset corresponding to these positions can be determined. These values are useful in analyzing the distribution of the data and identifying any outliers or patterns. For instance, if the 1st decile is much smaller or larger than the 9th decile, this may indicate an uneven distribution of the data or the presence of outliers.
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