Median of Grouped Data Worksheet
A Grade 11 math worksheet focused on calculating the median for grouped frequency distribution data, including practice problems and conceptual questions.
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Median of Grouped Data
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Read each question carefully and provide your answers in the space provided. Show all your work for calculations.
When data is presented in a frequency distribution table, we can estimate the median using a specific formula. Recall that the median is the middle value of a dataset when it is ordered. For grouped data, we first identify the median class, then use the formula:
Median = L + [((N/2) - C) / f] * h
Where:
L = Lower boundary of the median class
N = Total frequency
C = Cumulative frequency of the class preceding the median class
f = Frequency of the median class
h = Class width
1. Explain in your own words why we use a formula to estimate the median for grouped data, rather than finding the exact middle value.
2. For the formula Median = L + [((N/2) - C) / f] * h, the term N/2 represents the , and 'h' represents the .
3. The following table shows the distribution of scores of 50 students in a math test:
Scores (Class Interval)
Number of Students (Frequency)
0-10
5
10-20
12
20-30
15
30-40
10
40-50
8
Calculate the median score for this data.
4. In a grouped frequency distribution, if the cumulative frequency of the class preceding the median class is 25, and the (N/2)th item is 30, what does this imply?
The median class has a frequency of 5.
The median class is the first class.
The median class contains the 30th item.
The total frequency N is 30.
5. Consider the following frequency distribution of daily wages of 100 workers:
Daily Wages (RM)
Number of Workers
50-60
12
60-70
18
70-80
30
80-90
20
90-100
20
Determine the median daily wage.
6. The median for grouped data can sometimes be equal to the upper boundary of the median class.
True
False
7. Describe a scenario where calculating the median of grouped data would be more appropriate than calculating the mean.