Question

The latest antidepressant produced is currently involved in the testing process. Eight subjects have joined the testing process where the mean number of days taken before side effects disappeared is being examined. The results are as follows. 25, 12, 5, 16, 21, 10, 15, 9 What is the standard deviation (in days) of the sample

Answer 1

The standard deviation of a sample, use the formula
`s = sqrt((sum((X_i - X)^2))/(n-1)),` where s is the standard deviation,
`X_i` is each data point, X is the mean, and n is the number of data points. In this case, the mean is 14.125 and the standard deviation is approximately 6.56 days.

The standard deviation of a sample, you can use the following formula:

`s = sqrt((sum((X_i - X)^2))/(n-1))`

where:

• s is the sample standard deviation
• 
  `X_i` is each individual data point
• X is the mean of the sample
• n is the number of data points

Let's calculate it step by step:

1. Calculate the mean (X):

• (25 + 12 + 5 + 16 + 21 + 10 + 15 + 9) / 8 = 14.125

Calculate the squared difference from the mean
`((X_i - X)^2)` for each data point:

• 
  `(25−14.125)^2 =116.015625`

• 
  `(12 - 14.125)^2 = 4.265625`
• 
  `(5 - 14.125)^2 = 84.765625`
• 
  `(16 - 14.125)^2 = 3.390625`
• 
  `(21 - 14.125)^2 = 47.890625`
• 
  `(10 - 14.125)^2 = 17.015625`
• 
  `(15 - 14.125)^2 = 0.765625`
• 
  `(9 - 14.125)^2 = 26.015625`

Sum up the squared differences
`(sum((X_i - X)^2)):`

• 116.640625 + 4.265625 + 84.765625 + 3.390625 + 47.890625 + 17.015625 + 0.765625 + 26.015625 = 300.750000

Divide the sum by n-1 (7):

• 300.750000 / 7 = 42.9642857

Take the square root:

• sqrt(42.9642857) ≈ 6.559287

So, the standard deviation of the sample is approximately 6.56 days.

Answer 2

To find the standard deviation of the sample, calculate the mean, find the squared differences from the mean, add them up, divide by the number of values, and take the square root of the result.

Step-by-step explanation:

To find the standard deviation of the sample, you can follow these steps:

1. Calculate the mean of the sample by adding up all the values and dividing by the number of values. In this case, the mean is (25+12+5+16+21+10+15+9)/8 = 13.5 days.
2. Find the difference between each value and the mean, and square each difference. For example, the difference between 25 and the mean is 11.5, so the squared difference is 11.5^2 = 132.25.
3. Add up all the squared differences. In this case, the sum is 132.25 + 1.25 + 77.75 + 5.25 + 51.25 + 3.25 + 1.25 + 20.25 = 292.25
4. Divide the sum of squared differences by the number of values. In this case, 292.25/8 = 36.53.
5. Take the square root of the result to find the standard deviation. The square root of 36.53 is approximately 6.04 days.