Median of Grouped Data MCQs Quiz | Class 10
This quiz covers important Multiple Choice Questions (MCQs) on the Median of Grouped Data for Class X Mathematics (Code 041), Unit VII: Statistics & Probability. It focuses on identifying the median class and applying the formula for calculating the median in various numerical problems. Attempt all 10 questions, submit your answers, and download a detailed PDF of your responses and correct solutions.
Understanding Median of Grouped Data
The median is a measure of central tendency that represents the middle value of a data set. For grouped data, we cannot find the exact median, but we can determine a median class and then use a formula to estimate the median value within that class. This concept is crucial for understanding the distribution of data.
Key Concepts for Median of Grouped Data
- Median: The value that divides the data into two equal halves when arranged in ascending order. 50% of the observations are below it, and 50% are above it.
- Cumulative Frequency (cf): The sum of frequencies of a class and all classes below it. It helps in locating the median class.
- Median Class: The class interval in which the median lies. It is identified by finding the class whose cumulative frequency is just greater than or equal to N/2, where N is the total number of observations.
- Median Formula: The formula to calculate the median for grouped data is:
Median = L + [ (N/2 – cf) / f ] x h
Where:- L: Lower limit of the median class.
- N: Total number of observations (sum of all frequencies).
- cf: Cumulative frequency of the class preceding the median class.
- f: Frequency of the median class.
- h: Class size (width) of the median class.
Steps to Calculate the Median for Grouped Data
- Construct a cumulative frequency table for the given distribution.
- Calculate N (total number of observations) and then find N/2.
- Identify the median class: Locate the class interval whose cumulative frequency is just greater than or equal to N/2.
- Determine the values for L, N, cf, f, and h specific to the identified median class and the class preceding it.
- Substitute these values into the median formula and calculate the median.
Quick Revision Points
- Median is a position-based average, unlike mean which is value-based.
- Always arrange data (or ensure class intervals are ordered) before finding the median.
- The median always lies within the median class.
- The ‘cf’ in the formula is always the cumulative frequency of the class *before* the median class.
- ‘f’ is the frequency of the *median class itself*.
Practice Questions
Solve these additional questions to strengthen your understanding:
- Find the median class for the following data:
Class: 0-10, Frequency: 5
Class: 10-20, Frequency: 12
Class: 20-30, Frequency: 20
Class: 30-40, Frequency: 8 - Calculate the median for a distribution where L=45, N=100, cf=38, f=22, h=10.
- In a frequency distribution, if N=80 and the median class is 30-40, what would be the minimum possible cumulative frequency of the class preceding the median class?
- Explain why we need a cumulative frequency column to find the median of grouped data.
- A class has frequencies 10, 15, 20, 18, 7 for classes 0-20, 20-40, 40-60, 60-80, 80-100 respectively. Calculate the median.
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