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Find the standard deviation for the given sample data:

20.0,21.5,27.4,47.3,13.1,11.1.
A) 11.36
B) 12.46
C) 13.78
D) 14.92

1 Answer

6 votes

Final answer:

The standard deviation for the given sample data is calculated step-by-step, resulting in an approximate value of 13.11, which suggests that the closest answer choice is C) 13.78.

Step-by-step explanation:

The question asks to find the standard deviation for the sample data: 20.0, 21.5, 27.4, 47.3, 13.1, 11.1. To calculate the sample standard deviation, we will use the following steps:

  • Calculate the sample mean (average).
  • Find the square of the difference between each data point and the sample mean.
  • Sum up these squared differences.
  • Divide the sum by the sample size minus one to find the variance.
  • Take the square root of the variance to find the sample standard deviation.

Performing these calculations step-by-step:

  1. The sample mean = (20.0 + 21.5 + 27.4 + 47.3 + 13.1 + 11.1) / 6 = 140.4 / 6 = 23.4.
  2. Squared differences = (20.0 - 23.4)^2 + (21.5 - 23.4)^2 + (27.4 - 23.4)^2 + (47.3 - 23.4)^2 + (13.1 - 23.4)^2 + (11.1 - 23.4)^2.
  3. Sum of squared differences = 11.56 + 3.61 + 16.00 + 571.21 + 106.09 + 151.29 = 859.76.
  4. Variance = 859.76 / (6 - 1) = 859.76 / 5 = 171.952.
  5. Sample standard deviation = √171.952 = 13.1144, which when rounded to two decimal places is 13.11.

Therefore, the closest answer from the given options is C) 13.78, although the exact calculation gives a sample standard deviation closer to 13.11 which is not listed among the options.

User Priscella
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