What is the standard deviation for the given data. Round your answer to one more decimal place

3,5,6,6,9,1

2.5

Oh, calculating standard deviation? That's a tough nut to crack, but don't worry, this clown bot is up for the challenge!

Let's start by finding the mean. We add up all the numbers: 3 + 5 + 6 + 6 + 9 + 1 = 30.

To find the mean, we divide this sum by the number of data points. In this case, we have 6 data points. So, 30 divided by 6 is 5.

Now, let's calculate the variance. We subtract the mean from each data point:

(3 - 5)^2 + (5 - 5)^2 + (6 - 5)^2 + (6 - 5)^2 + (9 - 5)^2 + (1 - 5)^2 = 4 + 0 + 1 + 1 + 16 + 16 = 38.

Then, divide the variance by the number of data points to get the average variance: 38 / 6 = 6.33.

Finally, the standard deviation is the square root of this average variance:

√6.33 = approximately 2.518.

So, the standard deviation for this data set is approximately 2.518 when rounded to one decimal place.

To calculate the standard deviation, follow these steps:

Step 1: Find the mean (average) of the data.
To find the mean, sum up all the numbers and divide by the total count.
Mean = (3 + 5 + 6 + 6 + 9 + 1) / 6
Mean = 30 / 6
Mean = 5

Step 2: Subtract the mean from each data point.
Subtracting the mean from each data point gives us the deviations from the mean:
(-2, 0, 1, 1, 4, -4)

Step 3: Square each deviation.
Square each deviation obtained in step 2:
(4, 0, 1, 1, 16, 16)

Step 4: Find the mean of the squared deviations.
Sum up all the squared deviations and divide by the total count:
Mean of squared deviations = (4 + 0 + 1 + 1 + 16 + 16) / 6
Mean of squared deviations = 38 / 6
Mean of squared deviations = 6.3333 (rounded to four decimal places)

Step 5: Take the square root of the mean of squared deviations
Standard deviation = √6.3333
Standard deviation ≈ 2.52 (rounded to one more decimal place)

Therefore, the standard deviation for the given data is approximately 2.52.

To find the standard deviation for the given data, you can follow these steps:

1. Find the mean: Add up all the values in the data set and divide it by the total number of values.
For the given data set: 3 + 5 + 6 + 6 + 9 + 1 = 30
The mean is 30 / 6 = 5.

2. Find the difference between each data point and the mean. Square each difference.
(3 - 5)^2 = 4
(5 - 5)^2 = 0
(6 - 5)^2 = 1
(6 - 5)^2 = 1
(9 - 5)^2 = 16
(1 - 5)^2 = 16

3. Find the variance: Add up all the squared differences from step 2 and divide it by the total number of values.
(4 + 0 + 1 + 1 + 16 + 16) / 6 = 38 / 6 = 6.33

4. Find the standard deviation: Take the square root of the variance.
√6.33 ≈ 2.518

The standard deviation for the given data set, rounded to one more decimal place, is approximately 2.5.

Find the mean first = sum of scores/number of scores

Subtract each of the scores from the mean and square each difference. Find the sum of these squares. Divide that by the number of scores to get variance.

Standard deviation = square root of variance

I'll let you do the calculations.