Project Find a real-life data set and use the...

Question

Project Find a real-life data set and use the techniques of Chapter 2, including graphs and numerical quantities, to discuss the center, variation, and shape of the data set. Describe any patterns.

Accepted Answer

Hello there. Today we're going to solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. A survey records the number of hours 5 students spent on their English essay 79, 11, 8, and 10. Using this data, find the mean median range, standard deviation, and describe the shape of the distribution. Awesome. So it appears for this particular problem we're asked to solve for quite a few things. We're asked to find the mean, the median, the range, standard deviation, and the shape of the distribution. So we're gonna have 5 different answers. So with that in mind, let us first analyze our data set. So our data once again is 79, 11, 8, and 10. Let's solve for our mean first. Let's call the mean mu. So our mean mu in this case is going to be equal to us. We should recall, in order to solve the mean we need to add all of our data points together, so we need to add 797 + 9 + 11 + 8 + 10, and then we need to divide by the number of data points which is 5. And when we perform this calculation in our calculator, we will find that it's simply equal to 9, so that is one of our final answers. And let us now solve for the median, which, as we should recall, the median is the middle view, whereas our mean is the average. So in order to solve for the median, we need to sort the data from smallest number to largest number, so we need to write it as 7. 89, 10, and 11. And the middle value for this particular data set will be for our median, which I'll call capital M, our median will be simply equal to 9, because when we look at our middle. We will see when we go look for a middle number, we will get a value of 9. once again that is our middle value. Now we need to solve for the range, which I'll call simply R, and as you should recall, in order to solve for the range, we need to take the largest number, subtracted by the smallest number, so we need to take 11 minus 7, which will give us a value of 4. Now we need to solve for the standard deviation for our sample, and to do that we need to recall and use the following equation for our sample deviation which will denote as S. S is equal to the square root of 1 divided by N minus 1 multiplied by the sum of, so we need to take the sum. Of drum roll parenthesis. X subscript I minus X bar. To the power of 2. So once again S is equal to the square root of 1 divided by N minus 1 multiplied by the sum of parenthesis XI minus X to the power of 2. So it's important to note. That we already know the mean and the mean. Which is X bar is equal to 9, so that will mean that as we should also recall that N our number of samples is 5. So when we consider these values, we can now compute the squared deviations, and when we calculate the squared deviations, we can produce the following graph or rather the following table to help us organize our squared deviations. So we have our different values for X. So we have 789, 1011. Then we have our values for x minus X bar which will give us -2, -10, 12. Then we have X minus X bar to the power of 2, which will give us 41014 with a total sum of 10. So with that in mind, we can go ahead and state that S is equal to the square root of 10 divided by 4, which will be approximately equal to 1.58 when we plug that into our calculator in round to two decimal places. So that is one of our final answers. Hooray, we did it, so let's quickly Box our answers in green. So we have our mean, which was 9, our median, which was 9, and then finally we have our range, which was 4. And now we have our standard deviation, which is 1.58. So now our last answer that we're trying to solve for is the shape of the distribution. So once again we're told that our data points are 789, 1011, which means that they are evenly spaced because it goes 789, 1011, and we know that the mean equals the median, which equal, so the mean is equal to the median, which is equal to 9. So let's make a note of that. So our mean is equal to our median, which is equal to 9, and there are no outliers, which I'll just call O for short, so there's no outliers, and because the data is evenly spaced, the mean and median are equal to each other and there's no outliers. As we should recall, the shape will therefore Look like some so therefore the shape will be symmetric, the distribution will be symmetric. So Now that we've officially solved for all of our final answers, let's create a table to organize all of our answers, and when we create a table, it will look something along the lines of this. Where we'll have our column for the measure, and then our column for the value. And our value for the mean was 9, the value for the median was 9, the value for the range was 4. The standard deviation value was 1.58, and then the shape is symmetric. And that's it. We've officially solved for this problem. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

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Project Find a real-life data set and use the techniques of Chapter 2, including graphs and numerical quantities, to discuss the center, variation, and shape of the data set. Describe any patterns.

Key Concepts

Descriptive Statistics

Center of Data

Variation in Data

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