# Statistics Question - Find Standard Deviation of 5 numbers but only 4 given.

• JiHbE
In summary, the sample standard deviation for a sample of size 5 with values x1 - x̄ = -5, x2 - x̄ = 9, x3 - x̄ = -7, and x4 - x̄ = -2 is 6.305.
JiHbE
For a sample of size 5, if x1 - x̄ = -5, x2 - x̄ = 9, x3 - x̄ = -7, and x4 - x̄ = -2, then the sample standard deviation is:
a. 5.639
b. 6.782
c. None of the other answers are correct
d. 6.305
e. 6.066

Please note that x̄ is x-bar (mean of sample).

This question has been puzzling me. At first I thought there was an error because only 4 numbers are listed but it says there sample size is 5. But, this is a valid question.

So, I'm going to need the x5- x̄ value in order to calculate the standard deviation.
This is where I'm lost... could someone please provide some assistance?

Thank you so much for your time.

Can you express the mean in terms of x1 to x5? Rewriting that equation a bit will give you x5 - xmean.

JiHbE said:
For a sample of size 5, if x1 - x̄ = -5, x2 - x̄ = 9, x3 - x̄ = -7, and x4 - x̄ = -2, then the sample standard deviation is:
a. 5.639
b. 6.782
c. None of the other answers are correct
d. 6.305
e. 6.066

Please note that x̄ is x-bar (mean of sample).

This question has been puzzling me. At first I thought there was an error because only 4 numbers are listed but it says there sample size is 5. But, this is a valid question.

So, I'm going to need the x5- x̄ value in order to calculate the standard deviation.
This is where I'm lost... could someone please provide some assistance?

Thank you so much for your time.
Hello JiHbE. Welcome to PF !

What is $\ \ x_1+x_2+x_3+x_4+x_5-5\cdot\bar{x}\ ?$

Can you tell me how you typed x-bar? :)

What I do know is that:

mean = (x1 + x2 + x3+ x4 + x5)/5

Therefore,

5mean = (x1 + x2 + x3 + x4 + x5)

JiHbE said:
Can you tell me how you typed x-bar? :)
You can see the code via the "quote" button in his post.

Therefore,

5mean = (x1 + x2 + x3 + x4 + x5)
Right. Now you can use your knowledge about ##x_1-\bar{x}## and so on.

## 1. What is the formula for calculating standard deviation?

The formula for calculating standard deviation is √(Σ(x - x̄)² / (n-1)), where x is the individual data points, x̄ is the mean, and n is the sample size.

## 2. How do you find the standard deviation of 5 numbers when only 4 are given?

To find the standard deviation of 5 numbers when only 4 are given, you can follow these steps:

• Step 1: Find the mean of the 4 given numbers by adding them together and dividing by 4.
• Step 2: Calculate the sum of the squares of the differences between each number and the mean.
• Step 3: Divide the sum of squares by 3 (since there are only 4 numbers, n-1=3).
• Step 4: Take the square root of the result to find the standard deviation.

## 3. Why is the standard deviation important in statistics?

The standard deviation is important in statistics because it measures the spread of data around the mean. It helps to understand the variability within a data set and how much the data points differ from the average. It is also used to compare the spread of data between different data sets.

## 4. Can the standard deviation be negative?

No, the standard deviation cannot be negative. It is a measure of how far the data points are from the mean, so it will always be a positive value or 0 if all the data points are the same.

## 5. Is standard deviation affected by outliers?

Yes, standard deviation can be affected by outliers. Outliers are data points that are significantly different from the rest of the data. They can increase or decrease the standard deviation depending on their value and how far they are from the mean. It is important to consider outliers when interpreting the standard deviation of a data set.

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