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Calculate the median weight of students from the following frequency distribution table.
Mathematics
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Step-by-step solution
5 stepsCalculate the cumulative frequency (cf) for the given data.
Weight (kg) Number of students (f) Cumulative Frequency (cf) 40-45 9 9 45-50 5 9 + 5 = 14 50-55 8 14 + 8 = 22 55-60 9 22 + 9 = 31 60-65 6 31 + 6 = 37 65-70 3 37 + 3 = 40 The total number of students, .
Determine the median class.
The median position is .
The cumulative frequency just greater than or equal to 20 is 22, which corresponds to the class interval 50-55.
Therefore, the median class is 50-55.Identify the values for the median formula.
From the median class 50-55:
- Lower limit of the median class,
- Cumulative frequency of the class preceding the median class,
- Frequency of the median class,
- Class size,
Apply the median formula for grouped data.
The formula for the median is:
Substitute the values and calculate the median.
The median weight of the students is .
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