Answer:
64.5
Step-by-step explanation:
You understand the question, and already have the numbers in order, you're almost there!
So you need to find the median first so you can divide the data set into the upper and lower halves. The median, as you probably know, is the center of the data. What I do for this is list all the numbers out in order, like you've already done, and start crossing them out, one at a time, alternating the sides. I'll show you what I mean. (I'm using underline because there's no strikethrough.)
<u>52</u>, 54, 55, 55, 57, 58, 59, 59, 61, 61, 61, 62, 63, 63, 64, 65, 65, 68, 70, <u>72</u>
<u>52, 54</u>, 55, 55, 57, 58, 59, 59, 61, 61, 61, 62, 63, 63, 64, 65, 65, 68, <u>70, 72</u>
<u>52, 54, 55</u>, 55, 57, 58, 59, 59, 61, 61, 61, 62, 63, 63, 64, 65, 65, <u>68, 70, 72</u>
<u>52, 54, 55, 55</u>, 57, 58, 59, 59, 61, 61, 61, 62, 63, 63, 64, 65, <u>65, 68, 70, 72</u>
<u>52, 54, 55, 55, 57</u>, 58, 59, 59, 61, 61, 61, 62, 63, 63, 64, <u>65, 65, 68, 70, 72</u>
...and so on, until you have:
<u>52, 54, 55, 55, 57, 58, 59, 59, 61</u>, 61, 61, <u>62, 63, 63, 64, 65, 65, 68, 70, 72</u>
Because there's an even number of numbers, the median is the mean of the middle two numbers. Luckily, though, the two numbers in the middle are the same:61. Mean is calculated by adding the terms and dividing by the number of terms. In this case:
(61+61)/2
=61
(You didn't really have to do this mean step, but I'll explain later.)The median is 61. Another way you could have done this is by just counting the number of terms (20) and finding the middle one. Again, since there's no middle one, you'd have to find the mean.
Since you're looking for the third quartile and not the median, you didn't exactly have to do that step. I just wanted to explain how to calculate the median, since you'll have to do it in the next step. All we had to do here was divide the data set into the halves, so we used that visual demonstration by underlining the numbers one at a time. We didn't have to find the mean, we could have split the set down the middle instead.
<u>52, 54, 55, 55, 57, 58, 59, 59, 61, </u>61, | 61, <u>62, 63, 63, 64, 65, 65, 68, 70, 72</u>
^median/half-way point
We could have also divided the number of terms (20) by 2 (because halves, 2 parts) to get 10 and used the upper 10 values of the set, but I don't know, the crossing out method helps me. Anyway, now we have to look at just the upper 10 values:
61, 62, 63, 63, 64, 65, 65, 68, 70, 72
And you repeat the process! (I'm not going to show the underlining though lol)
There are 10 terms, so the median is between the 5th and the 6th. (10/2=5)
<u>61, 62, 63, 63</u>, 64, 65, <u>65, 68, 70, 72</u>
This is what I was talking about, there are an even number of values in the upper half of the data set as well, so we have to find the mean of the middle 2: 64 and 65.
(64+65)/2
=129/2
=64.5
That's your final answer. Hope I could help you!
