Math Problem Statement

median

The query submitted by the user: median

Solution

To calculate the median from the frequency distribution table you provided, follow these steps:

Steps:

  1. Find the cumulative frequency: We will first find the cumulative frequencies of the data to locate the median.

  2. Determine the position of the median: The median position is given by the formula: N+12\frac{N + 1}{2} where NN is the sum of the frequencies. In this case, N=60N = 60.

  3. 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 ItemFrequencyCumulative Frequency
01010
11525
21035
3944
4751
5556
6359
7160

2. Median Position:

60+12=612=30.5\frac{60 + 1}{2} = \frac{61}{2} = 30.5 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:

  1. How is the median different from the mean in such frequency distributions?
  2. What is the mode for this data set?
  3. How can we calculate the mean of this frequency table?
  4. Can the median change if we add more data items with different frequencies?
  5. 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