High School

We appreciate your visit to Consider the following data set that has a mean of 4 2 3 4 4 7 Using the equation below or the standard deviation formula. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

Consider the following data set that has a mean of 4:

2, 3, 4, 4, 7

Using the equation below or the standard deviation formula in Excel, calculate the standard deviation for this data set. Answer choices are rounded to the hundredths place.

\[ S = \frac{1}{n-1} \sqrt{\Sigma(x_i - \bar{x})^2} \]

a. 1.37
b. 1.87
c. 3.51
d. 2.12

Answer :

Final answer:

To calculate the standard deviation, subtract the mean from each value, square the results, sum them, divide by the number of values minus one, and take the square root. The calculated standard deviation for the given data set (2, 3, 4, 4, 7) with mean 4 is approximately 1.87. The correct answer is option b.

Explanation:

The subject of this question is Mathematics, specifically statistics involving the calculation of the standard deviation for a given data set. To calculate the standard deviation for a data set with a mean of 4 using the given numbers (2, 3, 4, 4, 7), we follow these steps:

  1. Subtract the mean from each number to find the deviations: (2-4), (3-4), (4-4), (4-4), (7-4).
  2. Square each deviation: (-2)^2, (-1)^2, 0^2, 0^2, 3^2.
  3. Sum the squared deviations: 4 + 1 + 0 + 0 + 9.
  4. Divide by the number of values minus one (N-1) which is 4: 14/4.
  5. Take the square root of the result to get the standard deviation: sqrt(14/4).

Carrying out the calculations:

  • Sum of squared deviations = 14
  • Variance (squared standard deviation) = 14/4 = 3.5
  • Standard deviation (s) = sqrt(3.5) ≈ 1.87

The correct answer is b. 1.87, rounded to the hundredths place.

Thanks for taking the time to read Consider the following data set that has a mean of 4 2 3 4 4 7 Using the equation below or the standard deviation formula. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada

Other Questions