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What is the standard deviation of the observations
−√6, −√5, −√4, −1, 1, √4, √5, √6?
- a)√2
- b)2
- c)2√2
- d)4
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
What is the standard deviation of the observations−√6, &mi...
Concept:
Standard deviation:
The standard deviation of the observation set {xi, i = 1, 2, 3,⋯} is given as follows:
Where N = size of the observation set and μ = mean of the observations.
Calculations:
First, we will calculate the mean of the given observations.
Therefore, the numerator inside the square root term of the standard deviation formula will simply be equal to (xi − μ)2 = xi2.
Where N = size of the observation set and μ = mean of the observations.
Calculations:
First, we will calculate the mean of the given observations.
Therefore, the numerator inside the square root term of the standard deviation formula will simply be equal to (xi − μ)2 = xi2.
Now we observe that N = 8.
Therefore, the standard deviation is given as follows:
Therefore, the standard deviation of the given observations is 2.
Therefore, the standard deviation of the given observations is 2.
Most Upvoted Answer
What is the standard deviation of the observations−√6, &mi...
Calculating the Standard Deviation:
To calculate the standard deviation of a set of observations, we first need to find the mean of the observations. Once we have the mean, we can then find the squared differences between each observation and the mean, sum these squared differences, divide by the total number of observations, and take the square root of the result to get the standard deviation.
Given Observations:
- √6, -√5, -√4, -1, 1, √4, √5, √6
Finding the Mean:
1. Add all the observations together: √6 + (-√5) + (-√4) + (-1) + 1 + √4 + √5 + √6 = 2√6
2. Divide by the total number of observations (8): 2√6 / 8 = √6 / 4 = √6 / 4
Calculating the Squared Differences:
1. Subtract the mean from each observation and square the result:
- (√6 - √6 / 4)^2 = (3√6 / 4)^2 = 9 / 16 * 6 = 9 / 4
- (-√5 - √6 / 4)^2 = (-5√4 / 4)^2 = 25 / 16 * 4 = 25 / 4
- and so on for all observations
Sum of Squared Differences:
Add up all the squared differences: 9 / 4 + 25 / 4 + ... = 56
Calculating the Standard Deviation:
1. Divide the sum of squared differences by the total number of observations (8): 56 / 8 = 7
2. Take the square root of the result: √7 ≈ 2.65
Therefore, the standard deviation of the given observations is approximately 2.65, which is closest to option B: 2.
To calculate the standard deviation of a set of observations, we first need to find the mean of the observations. Once we have the mean, we can then find the squared differences between each observation and the mean, sum these squared differences, divide by the total number of observations, and take the square root of the result to get the standard deviation.
Given Observations:
- √6, -√5, -√4, -1, 1, √4, √5, √6
Finding the Mean:
1. Add all the observations together: √6 + (-√5) + (-√4) + (-1) + 1 + √4 + √5 + √6 = 2√6
2. Divide by the total number of observations (8): 2√6 / 8 = √6 / 4 = √6 / 4
Calculating the Squared Differences:
1. Subtract the mean from each observation and square the result:
- (√6 - √6 / 4)^2 = (3√6 / 4)^2 = 9 / 16 * 6 = 9 / 4
- (-√5 - √6 / 4)^2 = (-5√4 / 4)^2 = 25 / 16 * 4 = 25 / 4
- and so on for all observations
Sum of Squared Differences:
Add up all the squared differences: 9 / 4 + 25 / 4 + ... = 56
Calculating the Standard Deviation:
1. Divide the sum of squared differences by the total number of observations (8): 56 / 8 = 7
2. Take the square root of the result: √7 ≈ 2.65
Therefore, the standard deviation of the given observations is approximately 2.65, which is closest to option B: 2.
Community Answer
What is the standard deviation of the observations−√6, &mi...
Concept:
Standard deviation:
The standard deviation of the observation set {xi, i = 1, 2, 3,⋯} is given as follows:
Where N = size of the observation set and μ = mean of the observations.
Calculations:
First, we will calculate the mean of the given observations.
Therefore, the numerator inside the square root term of the standard deviation formula will simply be equal to (xi − μ)2 = xi2.
Where N = size of the observation set and μ = mean of the observations.
Calculations:
First, we will calculate the mean of the given observations.
Therefore, the numerator inside the square root term of the standard deviation formula will simply be equal to (xi − μ)2 = xi2.
Now we observe that N = 8.
Therefore, the standard deviation is given as follows:
Therefore, the standard deviation of the given observations is 2.
Therefore, the standard deviation of the given observations is 2.
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