FORMULA CHAPTER
Lower class boundary = Lower class limit − d/2
Upper class boundary = Upper class limit + d/2
\text{Class Mark}=\frac{\text{Lower Class Limit}+\text{Upper Class Limit}}{2}
\text{Frequency Density}=\frac{\text{Class Frequency}}{\text{Class Size}}
\text{Percentage Frequency}=\frac{\text{Class Frequency}}{\text{Total Frequency}}\times100\%
Lower class boundary = Lower class limit − d/2
Upper class boundary = Upper class limit + d/2
Question: The class interval is 10–19 and the next class begins at 20. Find the class boundaries.
Calculation:
Step 1: d = 20 − 19 = 1.
Step 2: Lower boundary = 10 − 1/2 = 9.5.
Step 3: Upper boundary = 19 + 1/2 = 19.5.
Answer: The continuous class boundaries are 9.5 and 19.5.
\text{Class Mark}=\frac{\text{Lower Class Limit}+\text{Upper Class Limit}}{2}
Question: Find the class mark of the interval 20–30.
Calculation:
Step 1: Lower class limit = 20 and upper class limit = 30.
Step 2: Class Mark = (20 + 30) ÷ 2.
Step 3: Class Mark = 50 ÷ 2 = 25.
Answer: The class mark is 25.
\text{Frequency Density}=\frac{\text{Class Frequency}}{\text{Class Size}}
Question: A class interval of width 10 contains 40 observations. Find its frequency density.
Calculation:
Step 1: Class frequency = 40 and class size = 10.
Step 2: Frequency Density = Class Frequency ÷ Class Size.
Step 3: Frequency Density = 40 ÷ 10 = 4.
Answer: The frequency density is 4 observations per unit.
\text{Percentage Frequency}=\frac{\text{Class Frequency}}{\text{Total Frequency}}\times100\%
Question: In a distribution of 80 students, 20 students belong to one class interval. Find the percentage frequency.
Calculation:
Step 1: Class frequency = 20 and total frequency = 80.
Step 2: Percentage Frequency = (20 ÷ 80) × 100%.
Step 3: Percentage Frequency = 0.25 × 100% = 25%.
Answer: The percentage frequency is 25%.
