Math Problem Statement
median
Solution
To calculate the median from the frequency distribution table you provided, follow these steps:
Steps:
-
Find the cumulative frequency: We will first find the cumulative frequencies of the data to locate the median.
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Determine the position of the median: The median position is given by the formula: where is the sum of the frequencies. In this case, .
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Locate the median class: The cumulative frequency will help in identifying the median class, i.e., the data item where the median lies.
1. Constructing the cumulative frequency table:
Data Item | Frequency | Cumulative Frequency |
---|---|---|
0 | 10 | 10 |
1 | 15 | 25 |
2 | 10 | 35 |
3 | 9 | 44 |
4 | 7 | 51 |
5 | 5 | 56 |
6 | 3 | 59 |
7 | 1 | 60 |
2. Median Position:
This means the median is located between the 30th and 31st data items.
3. Identifying the median:
From the cumulative frequency table:
- The cumulative frequency reaches 25 at data item 1.
- The next cumulative frequency is 35, which occurs at data item 2.
Therefore, the median lies within the data item 2, as it contains the 30.5th value.
Conclusion:
The median is 2.
Would you like more details or have any questions?
5 Related Questions:
- How is the median different from the mean in such frequency distributions?
- What is the mode for this data set?
- How can we calculate the mean of this frequency table?
- Can the median change if we add more data items with different frequencies?
- How does the shape of the distribution affect the median?
Tip: The median is less affected by extreme values, making it a useful measure of central tendency for skewed distributions.
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Math Problem Analysis
Mathematical Concepts
Statistics
Frequency Distribution
Median Calculation
Formulas
Cumulative Frequency Formula
Median Position Formula: (N + 1) / 2
Theorems
Median Theorem
Suitable Grade Level
Grades 7-10