Mathematics

Mathematics

Problem

The frequency distribution of marks out of 50 obtained by 50 students in a Mathematics test is partially given below. The frequencies of the second and third classes are missing.
MarksFrequency
0 – 108
10 – 20a
20 – 30b
30 – 4012
40 – 506
It is known that: (i) The total number of students is 50. (ii) The frequency of the 10 – 20 class is half of that of the 20 – 30 class. Answer the following: (a) Determine the missing frequencies a and b. (b) Construct the cumulative frequency table using the complete set of frequencies. (c) Identify the median class and calculate the median mark for the test.
Intuitive explanation

This problem combines two fundamental ideas: using constraints to solve a system of equations, and understanding how cumulative frequencies reveal the central tendency of a dataset. You have two unknowns (aa and bb) and two pieces of information—the total count and a ratio relationship—which means you can set up and solve a linear system. Once you know all frequencies, cumulative frequency builds upward from the smallest marks, letting you pinpoint exactly where the middle student's score falls (the median class) and calculate the median using the standard formula.

Intuitive explanation

This problem combines two fundamental ideas: using constraints to solve a system of equations, and understanding how cumulative frequencies reveal the central tendency of a dataset. You have two unknowns (aa and bb) and two pieces of information—the total count and a ratio relationship—which means you can set up and solve a linear system. Once you know all frequencies, cumulative frequency builds upward from the smallest marks, letting you pinpoint exactly where the middle student's score falls (the median class) and calculate the median using the standard formula.

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