find the standard deviation for the given data. Round your answer to one more decimal place than original data. (9,7,13,24,32,45,47)

I get 16.62041 but how do I round my answer to one or more decimal places? I am a little lost.

Since the original data had 0 decimal places, according to the instructions I would round it off to 1 decimal place,

or 16.2

I meant to type 16.6

To round your answer to one more decimal place than the original data, you can follow these steps:

1. Calculate the standard deviation using the formula:
a. Find the mean of the data set.
b. For each value in the data set, subtract the mean and then square the result.
c. Find the average of the squared differences.
d. Take the square root of the average to obtain the standard deviation.

2. Once you have calculated the standard deviation, look at the number in the next decimal place after the existing decimal places of the original data.

3. If the number in the next decimal place is:
a. Less than 5, then you can keep the existing decimal places as they are.
b. 5 or greater, then you should increase the last existing decimal place by 1.

4. Round the standard deviation according to the rules above.

Applying these steps to the data (9, 7, 13, 24, 32, 45, 47):

1. Calculate the standard deviation using a mathematical software or tool, or manually.

- Sum of the data: 9 + 7 + 13 + 24 + 32 + 45 + 47 = 177
- Mean: 177 / 7 = 25.285714
- Subtract the mean and square the differences:
(9 - 25.285714)^2 = 263.959184
(7 - 25.285714)^2 = 282.938776
(13 - 25.285714)^2 = 151.489796
(24 - 25.285714)^2 = 1.612245
(32 - 25.285714)^2 = 44.591837
(45 - 25.285714)^2 = 403.816327
(47 - 25.285714)^2 = 472.183673
- Average of the squared differences: (263.959184 + 282.938776 + 151.489796 + 1.612245 + 44.591837 + 403.816327 + 472.183673) / 7 = 214.183673
- Square root of the average: √214.183673 ≈ 14.629857

2. The number in the next decimal place after the existing decimal places of the original data is 2.

3. Since 2 is less than 5, the existing decimal places can be kept as they are.

4. Therefore, rounding the standard deviation to one more decimal place than the original data gives us: 14.6.

To round your answer to one more decimal place than the original data, you need to examine the digit after the desired decimal place. In this case, you have calculated a standard deviation of 16.62041.

To round to one decimal place, you look at the digit in the second decimal place, which is a 2. Since 2 is less than 5, you can simply drop it and keep the first decimal place value unchanged. Therefore, rounding 16.62041 to one decimal place would give you a final answer of 16.6.

If you needed to round to two decimal places, you would consider the digit in the third decimal place, which is a 0. Since 0 is less than 5, you would drop it as well. Rounding 16.62041 to two decimal places would yield a final answer of 16.62.