QUANTILES OF FRACTILES

Fractiles, quartiles, deciles, and percentiles are terms used in statistics to describe different points that divide a dataset into various segments, helping to understand the distribution of data. Here’s a breakdown of each term:

1. Fractiles: Fractiles are points on a number scale that divide a dataset into specific portions. Quartiles, deciles, and percentiles are examples of fractiles. They help in analyzing the spread and characteristics of data.
2. Quartiles: Quartiles divide a dataset into four equal parts, each containing 25% of the data. There are three quartiles: Q1 (the 1st quartile) separates the lowest 25% of the data, Q2 (the 2nd quartile) is the median and separates the lowest 50%, and Q3 (the 3rd quartile) separates the lowest 75%. The 4th quartile is the highest 25% of data.
3. Deciles: Deciles divide a dataset into ten equal parts, each containing 10% of the data. For instance, the 1st decile represents the lowest 10% of values, the 3rd decile represents the lowest 30%, and the 5th decile is the median.
4. Percentiles: Percentiles divide a dataset into 100 equal parts, each containing 1% of the data. For example, the 25th percentile represents the value below which 25% of the data falls, the 50th percentile is the median, and the 75th percentile represents the value below which 75% of the data falls. The 100th percentile is the maximum value in the dataset.

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These concepts are particularly useful for understanding the distribution and characteristics of data, especially when analyzing large datasets or comparing data points across different datasets.

Starting with quartiles, they divide data into four equal parts. The 1st quartile has 25% of values below it, the 2nd quartile (median) has 50% of values below, the 3rd quartile has 75% below, and the 4th quartile (100%) encompasses all the values.

Moving on to deciles, they split the distribution into ten parts. The 1st decile has 10% of values below, the 3rd decile has 30%, and the 5th decile is the median.

Lastly, percentiles divide the data into 100 parts. The 1st percentile has 1% of values below, the 25th percentile is the same as the 1st quartile, the 50th percentile is the median, and the 75th percentile is the same as the 3rd quartile.

Next, we’ll delve into how to compute these quantiles or fractiles in the upcoming unit.

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Certainly, here are 15 fill-in-the-blank questions related to the topic of “Quantiles or Fractiles” along with options (a), (b), and (c):

1. A quartile divides data into _____ equal parts.
(a) two
(b) three
(c) four

2. The 2nd quartile is also known as the _____.
(a) median
(b) mean
(c) mode

3. The 1st quartile has _____ of values below it.
(a) 50%
(b) 25%
(c) 75%

4. The 10th decile has _____ of values below it.
(a) 30%
(b) 10%
(c) 50%

5. The 5th decile is the _____ of the distribution.
(a) median
(b) mean
(c) mode

6. The 25th percentile is equivalent to the _____ quartile.
(a) 1st
(b) 2nd
(c) 3rd

7. The 50th percentile is also known as the _____.
(a) mean
(b) median
(c) mode

8. The 75th percentile corresponds to the _____ quartile.
(a) 3rd
(b) 1st
(c) 2nd

9. The _____ percentile has 1% of observations below it.
(a) 25th
(b) 50th
(c) 1st

10. The 100th percentile encompasses _____ of the values.
(a) all
(b) 50%
(c) 25%

11. A quartile divides the data into how many groups?
(a) 3
(b) 4
(c) 5

12. What does the 3rd quartile represent?
(a) 75% below
(b) 50% below
(c) 25% below

13. The Sth decile is equivalent to the _____.
(a) 10th
(b) 5th
(c) 1st

14. What percentage of values are below the 50th percentile?
(a) 25%
(b) 50%
(c) 75%

15. What will be covered in the next unit regarding quantiles or fractiles?
(a) Definitions of quartiles
(b) Computation of quantiles
(c) Mean and standard deviation calculations

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Frequency Polygons and frequency curves

TERMS USED IN FREQUENCY DISTRIBUTIONS

Descriptive Statistics