High School

As of September 30, 2017, the earnings per share (EPS) of five firms in the biotechnology industry are:

1.53, 2.29, 2.07, 1.69, 0.07

The sample mean and the sample standard deviation are closest to:

A. 1.53 and 0.76
B. 1.53 and 0.87
C. 1.69 and 0.76
D. 1.69 and 0.87

Answer :

Final answer:

The sample mean is 1.53 and the sample standard deviation is approximately 0.999.

Explanation:

To calculate the sample mean, we need to sum up all the given EPS values and divide by the number of values. In this case, we have 5 values:

1.53 + 2.29 + 2.07 + 1.69 + 0.07 = 7.65

Next, we divide the sum by the number of values:

7.65 / 5 = 1.53

Therefore, the sample mean is 1.53.

To calculate the sample standard deviation, we need to find the squared differences between each data point and the mean, sum them up, divide by the number of values minus 1, and then take the square root of the result.

First, we calculate the squared differences:

[tex](1.53 - 1.53)^2 + (2.29 - 1.53)^2 + (2.07 - 1.53)^2 + (1.69 - 1.53)^2 + (0.07 - 1.53)^2 =[/tex] 0.0001 + 0.3136 + 0.1849 + 0.0289 + 2.4649 = 3.9924

Next, we divide the sum by the number of values minus 1:

3.9924 / (5 - 1) = 0.9981

Finally, we take the square root of the result:

√0.9981 ≈ 0.999

Therefore, the sample standard deviation is approximately 0.999.

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Final answer:

To find the sample mean and sample standard deviation of the earnings per share (EPS) for the given data, we can calculate the mean and find the squared differences from the mean, then calculate the sum and divide it by (n-1), where n is the number of values. Finally, take the square root of the result to get the sample standard deviation.

Explanation:

To find the sample mean and sample standard deviation of the earnings per share (EPS) for the given data, we can use the following steps:

  1. Calculate the sum of all the EPS values: 1.53 + 2.29 + 2.07 + 1.69 + 0.07 = 7.65
  2. Calculate the mean by dividing the sum by the number of values: 7.65 / 5 = 1.53
  3. For each value, subtract the mean and square the result
  4. Calculate the sum of the squared differences: (1.53 - 1.53)² + (2.29 - 1.53)² + (2.07 - 1.53)²+ (1.69 - 1.53)² + (0.07 - 1.53)² = 1.4694
  5. Divide the sum of squared differences by (n-1), where n is the number of values: 1.4694 / (5-1) = 0.36735
  6. Take the square root of the result to get the sample standard deviation: √(0.36735) = 0.6056

Therefore, the sample mean is 1.53 and the sample standard deviation is approximately 0.61.

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