Calculate the arithmetic mean of the following data: Class 10-... | Mathematics MCQ | Examoogle

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MathematicsStatistics

Calculate the arithmetic mean of the following data: Class 10-20 (Freq: 5), 20-30 (Freq: 10), 30-40 (Freq: 15), 40-50 (Freq: 10).

32.5

33.5

31.5

34.5

Correct Answer

📐 MA • Math Direct FormulaMathematicsStatistics

Option A

32.5

Quick Summary:

Use step-deviation method or direct mental calculation of products for smaller frequency tables to save time in the exam hall.

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📐MAMath SolutionDirect Formula

📋 Given

Class intervals 10-20, 20-30, 30-40, 40-50 with respective frequencies 5, 10, 15, and 10.

🔢 Formula Used

x‾=∑fixi∑fi\overline{x} = \frac{\sum f_i x_i}{\sum f_i}x=∑fi​∑fi​xi​​

⚡ Exam Hall Shortcut / Speed Trick

Use step-deviation method or direct mental calculation of products for smaller frequency tables to save time in the exam hall.

⚠️ Common Student Trap / Pitfall

Using class limits directly instead of calculating the class midpoints ( $x_i$ ) for each interval.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Find Class Midpoints

Calculate the midpoint $x_i$ for each class interval using the formula $x_i = \frac{\text{Lower Limit} + \text{Upper Limit}}{2}$ .

x1=15,x2=25,x3=35,x4=45x_1 = 15, x_2 = 25, x_3 = 35, x_4 = 45x1​=15,x2​=25,x3​=35,x4​=45

Calculate Product of Frequency and Midpoint

Multiply each frequency $f_i$ by its corresponding class midpoint $x_i$ and sum them up.

∑fixi=(5×15)+(10×25)+(15×35)+(10×45)=1300\sum f_i x_i = (5 \times 15) + (10 \times 25) + (15 \times 35) + (10 \times 45) = 1300∑fi​xi​=(5×15)+(10×25)+(15×35)+(10×45)=1300

Calculate Total Frequency

Sum up all the individual frequencies to find the total frequency $\sum f_i$ .

∑fi=5+10+15+10=40\sum f_i = 5 + 10 + 15 + 10 = 40∑fi​=5+10+15+10=40

Compute Arithmetic Mean

Apply the grouped data formula to find the final arithmetic mean.

x‾=130040=32.5\overline{x} = \frac{1300}{40} = 32.5x=401300​=32.5

✅

A is correct because the calculated arithmetic mean of the given grouped data is 32.5.

Core Concepts Used

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Arithmetic Mean for Grouped Data Class Midpoint Frequency Distribution

💡 EXAM TIP

Mastering grouped data statistics is foundational for data interpretation, median/mode calculations, and probability distributions in competitive exams.

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