Calculate the Variance (sigma2).

April 16, 2026Mathematics

ScanSolve AI Answer

April 16, 2026

Answer

51.2064

Step 1: Calculate the Variance ( $\sigma^2$ ). The formula for variance for grouped data is: $\sigma^2 = \frac{\sum f(x - \bar{x})^2}{\sum f}$ From the provided table, $\sum f(x - \bar{x})^2 = 2560.32$ and $\sum f = 50$ .

Substitute the values into the formula: $\sigma^2 = \frac{2560.32}{50}$ $\sigma^2 = 51.2064$

Step 2: Calculate the Standard Deviation ( $\sigma$ ). The standard deviation is the square root of the variance: $\sigma = \sqrt{\sigma^2}$ Substitute the calculated variance: $\sigma = \sqrt{51.2064}$ $\sigma \approx 7.156$

The variance is $\boxed{51.2064}$ The standard deviation is $\boxed{7.156}$

Send me the next one 📸

Was this helpful?

Need help with your own homework?

Get instant step-by-step solutions to any question. Free to start.

Ask Your Question

More Mathematics Questions

Q2 Find the value of x if 3x+4=19. 3 Find the value of y when 2y-7=21.QA teacher chooses 3 pens. The teacher randomly guesses a pen to use on an assignment. He, he will ke…QA. Write an equation and solve it. 1. Six times a certain number decreased by two is four times the…QWhen a certain number is increased by five, the result is six times the same number decreased by ten…QNumeric and geometric patterns. 1. Determine the constant difference or the constant ratio of the fo…

See all Mathematics questions →

Still have questions?

Quick Answer

Calculate the Variance (^2). The formula for variance for grouped data is: ^2 = f(x - x)^2 f From the provided table, f(x - x)^2 = 2560.32 and f = 50.

Asked on April 16, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on April 16, 2026

Step 1: Calculate the Variance (^2). The formula for variance for grouped data is: ^2 = f(x - x)^2 f From the provided table, f(x - x)^2 = 2560.32 and f = 50. Substitute the values into the formula: ^2 = (2560.32)/(50) ^2 = 51.2064 Step 2: Calculate the Standard Deviation (). The standard deviation is the square root of the variance: = sqrt(^2) Substitute the calculated variance: = sqrt(51.2064) ≈ 7.156 The variance is 51.2064 The standard deviation is 7.156 Send me the next one 📸

Asked on April 16, 2026Mathematics

ScanSolve AI AnswerAnswered on April 16, 2026

Step 1: Calculate the Variance (^2). The formula for variance for grouped data is: ^2 = f(x - x)^2 f From the provided table, f(x - x)^2 = 2560.32 and f = 50. Substitute the values into the formula: ^2 = (2560.32)/(50) ^2 = 51.2064 Step 2: Calculate the Standard Deviation (). The standard deviation is the square root of the variance: = sqrt(^2) Substitute the calculated variance: = sqrt(51.2064) ≈ 7.156 The variance is 51.2064 The standard deviation is 7.156 Send me the next one 📸