Finding the median in a frequency table involves locating the middle value of the data set represented by the table. Here's a step-by-step guide:
Steps to Find the Median in a Frequency Table
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Calculate the Total Frequency (N): Sum up all the frequencies in the frequency table. This gives you the total number of data points.
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Determine the Median Position: Calculate the position of the median using the formula: (N + 1) / 2. This formula tells you which value in the ordered data set represents the median.
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Identify the Median Class: Use the cumulative frequency column (if available, or create one) to find the class interval that contains the median position calculated in step 2. The cumulative frequency for each class represents the total number of data points up to and including that class. Find the class where the cumulative frequency is equal to or just exceeds the median position.
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Calculate the Median (if required): If you need a specific value for the median (rather than just the median class), you can use the following formula, also known as interpolation:
- Median = L + [ ( (N/2) - CF ) / f ] * w
Where:
- L = Lower boundary of the median class
- N = Total frequency
- CF = Cumulative frequency of the class before the median class
- f = Frequency of the median class
- w = Class width of the median class
Example
Let's say we have the following frequency table:
| Class Interval | Frequency (f) | Cumulative Frequency (CF) |
|---|---|---|
| 10-20 | 5 | 5 |
| 20-30 | 8 | 13 |
| 30-40 | 12 | 25 |
| 40-50 | 7 | 32 |
| 50-60 | 3 | 35 |
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Total Frequency (N): N = 5 + 8 + 12 + 7 + 3 = 35
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Median Position: (N + 1) / 2 = (35 + 1) / 2 = 18
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Identify the Median Class: The cumulative frequency of 13 is less than 18, but the cumulative frequency of 25 is greater than 18. Therefore, the median class is 30-40.
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Calculate the Median (using interpolation):
- L = 30 (lower boundary of the median class)
- N = 35
- CF = 13 (cumulative frequency of the class before the median class)
- f = 12 (frequency of the median class)
- w = 10 (class width of the median class)
Median = 30 + [ ( (35/2) - 13 ) / 12 ] 10
Median = 30 + [ (17.5 - 13) / 12 ] 10
Median = 30 + [ 4.5 / 12 ] 10
Median = 30 + 0.375 10
Median = 30 + 3.75
Median = 33.75
Therefore, the median value is 33.75.
In summary, finding the median in a frequency table involves determining the median position based on the total frequency and then locating the corresponding class interval. If desired, interpolation can provide a more precise median value.
