Questions: Consider the following data: 9,11,8,14,7,5 Step 2 of 3: Calculate the value of the sample standard deviation. Round your answer to one decimal place.

Consider the following data: 9,11,8,14,7,5 Step 2 of 3: Calculate the value of the sample standard deviation. Round your answer to one decimal place.
Transcript text: Consider the following data: \[ 9,11,8,14,7,5 \] Step 2 of 3: Calculate the value of the sample standard deviation. Round your answer to one decimal place.
failed

Solution

failed
failed

Solution Steps

Step 1: Calculate the sample mean (\(\bar{x}\))

To find the sample mean, sum all the data points and divide by the number of data points (n=6). \[\bar{x} = \frac{1}{6} \sum_{i=1}^{6} x_i = 9\]

Step 2: Calculate the variance

Subtract the mean from each data point, square the result, sum all those squared differences, and then divide by \(n-1\). \[\text{Variance} = \frac{1}{6-1} \sum_{i=1}^{6} (x_i - \bar{x})^2\]

Step 3: Calculate the sample standard deviation

Take the square root of the variance. \[s = \sqrt{\text{Variance}} = 3.2\]

Final Answer:

The sample standard deviation of the dataset, rounded to 1 decimal places, is 3.2.

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
What term refers to the size of a form in an artwork relative to its actual real-world dimensions? scale rhythm visual weight proportion
failedAnswered
Solve the system if possible by using Cramer's rule. If Cramer's rule does not apply, solve the system by using another method. Write all numbers as integers or simplified fractions. x-2y+3z = -1 5x-7y+3z = 1 x - 5z = 2 Part 1 of 2 Evaluate the determinants Dy Dx, Dy, and Dz.
failedAnswered
Compute the directional derivative of the following function at the given point P in the direction of the given vector. Be sure to use a unit vector for the direction vector. f(x, y) = ln(2+x^2+2y^2); P(3,-1); <3,1> Find the gradient of f(x, y) = ln(2+x^2+2y^2). ∇f(x, y) = square, square The directional derivative is square (Type an exact answer, using radicals as needed.)
failedAnswered
Which of the following shapes are quadrilaterals? Choose 2 answers: A B C D
failedAnswered
Multiple Choice Question How do scientists determine whether the results of an experiment differ between an experimental group and a control group? They reduce the system to its parts, and examine molecular patterns. They assume that their hypothesis is correct and interpret the data accordingly. They replicate the experiment to determine if they can achieve the same results. They analyze the data with statistics.