A sample of college students was asked how much they spent monthly on a cell phone plan (to the nearest dollar). Find the mean and standard deviation of the following quantitative frequency distributions. Monthly Cell Phone Plan Cost ($) Number of Students 10 - 19 8 20 - 29 16 30 - 39 21 40 - 49 11 50 - 59 4
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Answer:
In problem three. We have the frequency distribution for the monthly cellphone plan costs in dollars. Given for a sample of college students, which means the frequency he represents, the number of students we want to estimate or approximate the mean and standard division for the cost to do so we can can create them in which equals the submission for the frequency, multiplied by the midpoint of each close divided by as a mission of the frequency. This means we need to calculate the midpoint of each clothes first. That's a column for the midpoint of each clause, which can be calculated using the lower limits of the close range. The lower limit here and the lower limit here. It's the average between two consecutive lower limits. The average of 10 plus 20 equals 15. And simply we can add then which is the difference between these two values 4 15. to get the second midpoint 25 at 10. Again 35 at 10. Then it's 55 years. And we want to get another column for the multiplication of F. And X. The frequency and the midpoint if but the blade by X. It's it multiplied by 15 which he gives 120. Then we have 400 Which is 16. multiplied by 25. And so then we have sorry 735. Then 495 and 20. 220. And we need to calculate the submission for F. Multiplied by X. Submission. Is to calculate the some of each value. Here we add all these values together in this column To get the submission which is 1009. 107, divided by some mission of F. Which means we need to calculate the submission of the frequency or the number of students engaged in this study which is six. Then the mean can be calculated as submission of F. To blow it by X. Divided by submission of F. Then the answer is 32.8 dollars. Of course this is the average cost. To get the standard division. We can use the formula. It equals square root for the submission of F. Multiplied by X square minus some mission of F. Multiplied by X. Old square divided by submission of F. Divided by the submission of F -1. Don't forget -1. Because this is assembly, not the not the population. Then We need to account for this -1. We have all values except for F. Multiplied by X squared. Which means we need to add another column to get F. Multiplied by X squared. We square each X value here, then multiply it by the corresponding frequency. Then we have for the 1st 15 squared but employed by it gives 1000 And 800 and so on. Then the next value is 25 squared lined by 16 Which is 10,000, 10,000. Then we have 25,725 22,000 275 and 75. And finally yeah 12,100. And of course we have the submission sign here we add all the values of this column together to get the submission Which is 71,900. Let's substitute by the values. It's the square root of submission of F. X. Square given here minus submission of X. Square, submission of F. Multiplied by X. Square. We take this value and square it divided by submission of X. Take submission of F. Sorry We take this value to 16, Divide by 60 -1. Then it equals 10.97 or approximately equals 11 point oh course dollars. Then this is the average cost or the mean because for the monthly cellphone plan and this is the standard deviation