Calculate the population standard deviation of the data 13, 17... | Mathematics MCQ | Examoogle

Examoogle • User • info@examoogle.com • EE-2024-8821

Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked

MathematicsStatistics

Calculate the population standard deviation of the data 13, 17, 23, 26, 31, 28, 15, 34, 17, and 26. (Round off your answer to two decimal places.) 7286

7.18

7.26

6.81

6.19

Correct Answer

📐 MA • Math Direct FormulaMathematicsStatistics

Option C

6.81

Quick Summary:

Calculate the mean first, then use the variance shortcut formula $\sigma^2 = \frac{\sum x_i^2}{n} - \overline{x}^2$ . This avoids repeated subtraction errors.

🎯

Crack Statistics with Examoogle SuperTeachers

Get Free Demo Classes & Live Mocks →

📐MAMath SolutionDirect Formula

📋 Given

A data set of 10 values: 13, 17, 23, 26, 31, 28, 15, 34, 17, and 26.

🔢 Formula Used

σ=∑i=1n(xi−x‾)2n\sigma = \sqrt{\frac{\sum_{i=1}^{n} (x_i - \overline{x})^2}{n}}σ=n∑i=1n​(xi​−x)2​​

⚡ Exam Hall Shortcut / Speed Trick

Calculate the mean first, then use the variance shortcut formula $\sigma^2 = \frac{\sum x_i^2}{n} - \overline{x}^2$ . This avoids repeated subtraction errors.

⚠️ Common Student Trap / Pitfall

Confusing 'Population Standard Deviation' (divide by $n=10$ ) with 'Sample Standard Deviation' (divide by $n-1=9$ ), which leads to an incorrect higher value.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Calculate the mean

Sum of all values is $13+17+23+26+31+28+15+34+17+26 = 230$ . The mean is $230/10 = 23$ .

x‾=23\overline{x} = 23x=23

Calculate squared deviations from mean

Subtract mean from each value and square: $(13-23)^2=100, (17-23)^2=36, (23-23)^2=0, (26-23)^2=9, (31-23)^2=64, (28-23)^2=25, (15-23)^2=64, (34-23)^2=121, (17-23)^2=36, (26-23)^2=9$ .

∑(xi−x‾)2=464\sum (x_i - \overline{x})^2 = 464∑(xi​−x)2=464

Calculate variance and standard deviation

Divide sum of squares by $n=10$ to get variance $\sigma^2 = 46.4$ , then take the square root.

σ=46.4≈6.8117\sigma = \sqrt{46.4} \approx 6.8117σ=46.4​≈6.8117

✅

C is correct because the square root of the variance ( $46.4$ ) equals approximately 6.81.

Core Concepts Used

Click any tag to open in AI Tutor

Mean calculation Variance Population Standard Deviation

💡 EXAM TIP

Standard deviation is the square root of variance, a concept frequently tested in Data Interpretation sections of competitive exams to measure data dispersion.

Was this solution helpful?

⚡ Practice on Android App · 4.8 ★

Solve 10,000+ More Questions with AI Tutor

Get instant step-by-step AI explanations, full shift Previous Year Papers (SSC GD, RRB, SSC JE), and regional rank analysis on the official Examoogle App.

Free Download • 100K+ Aspirants

Discussion (0)

Loading discussion...

Prev Next

Correct Answer

Solve 10,000+ More Questions with AI Tutor

Related Questions

Discussion (0)