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Questions and Answers
What is the formula to calculate the lower quartile for a discrete frequency distribution?
How is the median (Q2) calculated for a continuous frequency distribution?
In the context of grouped data, what does the Lower Quartile (Q1) represent?
What role does the Class Width play in calculating quartiles for continuous frequency distributions?
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What happens to the lower limit of the third quartile class when calculating the Upper Quartile for continuous frequency distributions?
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Which formula is used to calculate the median (Q2) for a discrete frequency distribution?
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Study Notes
Quartiles for Grouped Data: Calculation
Quartiles help to divide a dataset into four equal parts, each containing an equal proportion of data. They are commonly used to describe the distribution of continuous data. In the context of grouped data, quartiles are calculated differently than they are for ungrouped data. To calculate quartiles for grouped data, follow these formulas:
-
Lower Quartile:
- For discrete frequency distribution:
Q_1 = \dfrac{2(N)}{4} = \dfrac{N}{2} - For continuous frequency distribution:
Q_1 = l + h \times \dfrac{N_1}{N} - where:
- N: Total number of observations
- l: Lower limit of the first quartile class
- h: Class width
- For discrete frequency distribution:
-
Median (Second Quartile):
- For discrete frequency distribution:
Q_2 = \dfrac{N + 1}{2} - For continuous frequency distribution:
Q_2 = l + \dfrac{N_2 - N_1}{2N} - where:
- N: Total number of observations
- l: Lower limit of the first quartile class
- N_1: Cumulative frequency of the first quartile class
- N_2: Cumulative frequency of the second quartile class
- For discrete frequency distribution:
-
Upper Quartile:
- For discrete frequency distribution:
Q_3 = \dfrac{3(N)}{4} = \dfrac{3N}{4} - For continuous frequency distribution:
Q_3 = l + h \times \dfrac{N_3 - N_2}{N} - where:
- N: Total number of observations
- l: Lower limit of the third quartile class
- h: Class width
- For discrete frequency distribution:
These formulas are derived from the requirement that the quartiles divide the data into four equal parts. The lower quartile is the 25th percentile, the median is the 50th percentile, and the upper quartile is the 75th percentile. By calculating these quartiles, we can gain a better understanding of the distribution of data and how it is spread across different values.
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Description
Learn how to calculate quartiles for grouped data using specific formulas for lower quartile, median (second quartile), and upper quartile. Understand the difference in calculations for discrete and continuous frequency distributions, and how quartiles help divide data into four equal parts.
