Question

Find the mandard deviation for the given sample data. 4) The top nine seopes on the arganic dhemivary midterm are as followe: 4) \( 30,34,25,41,72,22,53,31,20 \)

Answer 1

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

1. Calculate the mean (average) of the data.
2. Subtract the mean from each data point and square the result.
3. Calculate the mean of the squared differences.
4. Take the square root of the mean from step 3 to find the standard deviation.

Let's calculate the standard deviation for the given sample data:

Step 1: Calculate the mean
Mean = (30 + 34 + 25 + 41 + 72 + 22 + 53 + 31 + 20) / 9
Mean = 328 / 9
Mean ≈ 36.44

Step 2: Subtract the mean and square the result
(30 - 36.44)² = 42.79
(34 - 36.44)² = 5.96
(25 - 36.44)² = 131.27
(41 - 36.44)² = 20.46
(72 - 36.44)² = 1270.28
(22 - 36.44)² = 209.16
(53 - 36.44)² = 273.70
(31 - 36.44)² = 29.52
(20 - 36.44)² = 267.16

Step 3: Calculate the mean of the squared differences
Mean = (42.79 + 5.96 + 131.27 + 20.46 + 1270.28 + 209.16 + 273.70 + 29.52 + 267.16) / 9
Mean = 2259.30 / 9
Mean ≈ 251.03

Step 4: Take the square root of the mean
Standard Deviation = √(251.03)
Standard Deviation ≈ 15.84

Therefore, the standard deviation for the given sample data is approximately 15.84.