Standard Deviation One way to get a very rough approximation o...

Question

Standard Deviation One way to get a very rough approximation of the value of a standard deviation of sample data is to find the range, then divide it by 4. The range is the difference between the highest sample value and the lowest sample value. In using this approach, what value is obtained from the sample data listed in Exercise 1 “IQ Scores”?

Accepted Answer

Hello everyone. Let's take a look at this question together. A quick way to estimate the standard deviation of a sample is to take the range, which is the difference between the highest and lowest values, and divide it by 4. Using this method, what approximate standard deviation is obtained from the following test scores of randomly selected students. And the test scores are as followed. 76, 89, 94, 85, 92, 80, 88, 91, 95, and 78 is the approximate standard deviation. Answer choice A 3.25, answer choice B, 4.75, answer choice C 5.50, or answer choice D 6.25. So in order to solve this question, we have to calculate the approximate standard deviation from the test scores of the randomly selected students by taking the range of the values and dividing it by 4, which first we can calculate the range as the maximum or highest value, subtracted by the minimum or the lowest value. Which, looking at the test scores, we know that the maximum or highest value is 95, and the minimum or lowest value is 76. Therefore, we calculate 95 subtracted by 76, which equals 19, so the range is equal to 19, and to calculate the standard deviation. We take the range divided by 4, which can be calculated as 19 divided by 4, which is equal to 4.75. So the approximate standard deviation is 4.75, making answer choice be the correct answer, and all other answer choices are incorrect. I hope you found this video to be helpful. Thank you and goodbye.

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Key Concepts

Standard Deviation

Range

Approximation Method for Standard Deviation

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