Math Problem Statement
Solution
Let’s address the questions presented in the table and calculations step-by-step.
(a) Based on Table 4:
(i) Kelas Mod (Mode Class)
The mode class is the class interval with the highest frequency. From the table:
- The class interval 40–49 has the highest frequency (12 students).
Answer: Kelas Mod = 40–49
(ii) Saiz Selang Kelas (Class Interval Size)
The size of a class interval is calculated by: Using the first interval, :
Answer: Saiz Selang Kelas = 10
(iii) Julat (Range)
The range is the difference between the largest and smallest values in the dataset: From the table:
Answer: Julat = 59
(b) Calculate the Median (without drawing an ogive)
The median class is determined as the class interval containing the cumulative frequency equal to or just exceeding , where is the total number of students.
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Find Total Frequency (): Add all frequencies:
-
Determine :
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Locate the Median Class: Cumulative frequencies:
- 10–19: 3
- 20–29:
- 30–39:
- 40–49:
The cumulative frequency exceeds in the class interval 40–49, so this is the median class.
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Apply Median Formula: Where:
- (lower boundary of median class)
- (cumulative frequency before median class)
- (frequency of median class)
- (class size)
Substitute values:
Answer: Median ≈ 42.83
Would you like further clarifications or breakdowns for any of these calculations? Here are some related questions you might explore:
- How do we calculate the mean for this dataset?
- What is the significance of choosing the median over the mode or mean?
- How would an ogive be plotted for this dataset?
- How can we use cumulative frequency tables to find other percentiles?
- What happens if the intervals are uneven in width?
Tip: Always check the class intervals for consistency before performing statistical calculations.
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Math Problem Analysis
Mathematical Concepts
Statistics
Mode
Median
Class Intervals
Formulas
Class Size = Upper Boundary - Lower Boundary + 1
Range = Maximum Value - Minimum Value
Median = L + ((N/2 - F)/f) × c
Theorems
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Suitable Grade Level
Grades 10-12