Find the standard deviation for the given data. Round your answer to one more decimal place than the original data.

15, 42, 53, 7, 9, 12, 14, 28, 47
A. 29.1

B. 16.6

C. 17.8

D. 15.8

is it C

First find the mean, μ where

μ = (sum of all numbers, Σxi)/(number of values, N)

Standard deviation, σ, is given by
σ²=(sum of (xi-μ)²)/N
and finally
σ=sqrt(σ²)

Correction:

The equation given above
σ²=(sum of (xi-μ)²)/N
applies to a population.

C is correct if we interpret the data as a sample of the given population, in which case the standard deviation is given as:
σ²=(sum of (xi-μ)²)/(N-1)
= 17.8

To find the standard deviation of a set of data, follow these steps:

Step 1: Find the mean (average) of the data set.
To find the mean, add up all the numbers in the data set and divide the sum by the total number of values.

For the given data: 15, 42, 53, 7, 9, 12, 14, 28, 47
Sum = 15 + 42 + 53 + 7 + 9 + 12 + 14 + 28 + 47 = 227
Total number of values = 9
Mean = Sum / Total number of values = 227 / 9 = 25.2

Step 2: Calculate the deviation of each data point from the mean.
To find the deviation, subtract the mean from each data point.

For example, for the first data point (15): 15 - 25.2 = -10.2

Step 3: Square each deviation.
Square each deviation obtained in step 2.

For example, for the first data point: (-10.2)^2 = 104.04

Step 4: Find the sum of all squared deviations.
Add up all the squared deviations obtained in step 3.

For example, adding up all the squared deviations for the given data set:
104.04 + 307.44 + 702.24 + 332.82 + 261.36 + 146.41 + 94.09 + 5.76 + 441.00 = 2394.16

Step 5: Divide the sum of squared deviations by the total number of values.
Divide the sum of squared deviations obtained in step 4 by the total number of values.

For example, for the given data set: 2394.16 / 9 = 266.016

Step 6: Take the square root of the result obtained in step 5.
Take the square root of the result obtained in step 5. This will give you the standard deviation.

For example, for the given data set: square root of 266.016 ≈ 16.31

Now, let's round the standard deviation to one more decimal place than the original data.

The original data provided has one decimal place. So, rounding the standard deviation to one more decimal place, we get:

16.3

Therefore, the correct answer is B. 16.6.

C is not correct. There is a choice which is close to the answer.

The previous post shows how you can find the correct answer.