Problem

Teacher raises Refer to Exercise $20 .$ If each t…

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Problem 21 Medium Difficulty

Tall or short? Refer to Exercise 19. Mr. Walker converts his students’ original heights from inches to
feet.
(a) Find the mean and median of the students’ heights in feet. Show your work.
(b) Find the standard deviation and IQR of the students’ heights in feet. Show your work.

Answer

a. $\mu \approx 5.766$
$M E D I A N \approx 5.792$

b. $\sigma \approx 0.267$
$I Q R \approx 0.271$

Boris M.

University of North Carolina at Chapel Hill

Intro Stats / AP Statistics Courses

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Video Transcript

this'll question is based on basics. Right when you multiply or divide all off your observations by a constant, let's say B. You mean your median, your percentiles? Everything is multiplied by a factor off feet, but what happens is your standard deviation and all of these things they get multiplied by smart off. This is what we're going to use over here. We have been given a few observations in one of the previous questions. Question number 19. So what is given to us, I mean, is 69 point when it did, I mean is 69.188 right? But this has given inches. This has given an inch. Is now we want What are they saying? We want to find the mean and median in feet. Now 12 inches is equal to 1 ft. 12 inches is equal to 1 ft, which means that whatever I have an interest, I'm going toe. Have to divide by 12, right? What happens to the meeting? Well, meaning simply divided or multiplied by the factor off be as we have just seen, so are mean in feet is going to be 69.188 divided by 12, which happens to be, what, 5.766 Approximately 5.766 Okay, now in that table, what is the medium that is given to us? 69.5 median is given as 69.5. Right? The media has given us 69 point fight. All right, we are going to divide this by 12. And the answer that we get is 5.7, 90 5.792 Right. I think this was part eight. Now moving on the part B. What is part we have to say now we want to calculate the standard deviation. Okay, over there. The standard deviation. Waas 0.32 Sure 0.3 to 0. So our sigma there waas 0.3 to 0. But again, this was an inch is right. This was an interest. So this was 3.2 divided by 12. What do I get? I am going to again divide this right 12 in feet if I want. This thing is in feet. This thing is also in feet now in feet. This is going to be 3.2 divided by 12 feet. Right. Which becomes around. Let me write this as 2.7. Very close to 2.7. Okay. All right. What is going to be the Inter one for quartile range? I Q r my i Q r In that case, in the table. I can see that. My Urs. I love to calculate this. This actually is Q three minus Cuba is que three minus Cuban. What is Q 3 71. Q one is 67.75 So this is 71 minus 67 point still in faith. Okay, so what does this become? 71 minus 67.75 This is 3.25 This is 3.25 Okay? Yeah, But again, remember that this isn't this thing isn't inches. Now, if I want this to be in feet again, have to divide this by 12. So this is going to be three point to fight by 12 feet, right? So 3.25 divided by 12, which is 0.2708 Okay, this happens to be point 27080 point 27083 Okay, this is my I Q. Are in feet. My, I Q are in feet. These are my answers. This is actually point 2666 and so on. Right? That's why I returned. It has point to 6.27 but okay, let's write Write it like this. Okay? This is how we go about doing this question.

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