From a random sample of airplanes, the number of defects found...

Question

From a random sample of airplanes, the number of defects found in their fuselages are listed. Find the sample mean and the sample standard deviation of the data.

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Accepted Answer

Hello everyone. Let's take a look at this question together. Inspectors recorded the number of paint scratches found on a sample of new cars. The table below shows the number of scratches and the number of cars with that count. Find the sample mean and sample standard deviation for the number of scratches per car. And here we have our data table of the number of scratches and the number of cars. So in order to solve this question, we have to recall how to find the sample mean and the sample standard deviation so that we can determine the mean and sample standard deviation for the number of scratches per car using the following data table. And so the first step is to calculate the sample mean using the formula for the sample mean, which is X bar is equal to the sum of X multiplied by F divided by n, and we know that in the given data table the number of scratches is X and the corresponding number of cars with that count. F and the value for N, which is the sample size, is equal to the total frequency. Therefore, N is equal to the sum of F, which can be calculated using the values for the number of cars. So we add all of those values together, giving us our sample size N of 20. And then we can calculate the sample mean using that formula that we have for the sample mean, and substituting our values for the sum of X multiplied by F divided by N, which plugging in the values from the data table, our sample mean is equal to 1.8. And now that we have calculated the sample mean, we can calculate the sample standard deviation, which we know that the formula for the sample standard deviation is S is equal to the square root of the sum of the X minus X bar squared values multiplied by F divided by n. Minus 1. And so substituting the values into the sample standard deviation formula, we have S is equal to the following values in the numerator divided by 20 minus 1, which when calculated the value for S is approximately 1.3. So our sample standard deviation value is 1.3. Therefore, from the following data table of the number of scratches per car, our sample mean, which is X bar, is equal to 1.8, and our sample standard deviation is equal to 1.3. And looking at our answer choices, we can identify that answer choice A is 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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