Measures of Dispersion From a Frequency Table
Measures of dispersion from a frequency table.
Okay in this video we are gonna be looking at finding the measures of a dispersion. So that?s range and quarter range and instead of deviation from a table. <br> So we?ve been given a 00:14 here. It?s a small table with scores and the frequency each score. And what you need to do is you need to expand this table out. So we got the columns for scoring frequency. You also then need to add another 4 columns. Okay. So all I?ve done is I?ve taken this table here, I?ll put this values in. My columns for scores and frequency and added 4 more columns. This column is looking at kilometer frequency. The next one is going to be score times of frequency. This one here is looking at score squared, and this one is looking at the score squared times the frequency. <br> So we?re gonna quickly go through filled this table out. Down here let?s find the total of the frequencies that we add all of this up. That?s 10, 20, 30, 40, fifty--seven. You can put that in. So it?s gonna be 57. There is 57 data items in your ---- <br> So let?s look at kilometer frequency, so we got 3 plus another 4 gives us 7 plus another 6 gives us 13, 20, 28, 37, 43, 51, 55, and 57. So this value are the same which is good. <br> Now let?s see if we get to multiply the first two columns together to fill out the 4th column. Say 7 times 3 is 21, 8 times 4 is 32, 9 times 6 is 54, 10 times 7 is 70, 11 times 8 is 88, 12 times 9, 108, 13 times 6, 78, 14 times 8, 112, 15 times 4, 60, 16 times 2 is 32. And we go through and add all these values up together. 655 is the total for that column there. <br> Alright with this next form we?re gonna simply get the score and we?re gonna square it. So 7 squared is 49, 64, 81 and 100. That?s a 121, 144, 169, 196, 225 and 256. <br> Okay, the last column we?ll looking at multiplying the second column by the fifth column here. So 3 times 49 that?s 147, 4 times 64, 256, 6 times 81, 486, 7 times a hundred, 700, 8 times a 121, 968, 9 times 144 is 1296, 6 times 169, 1014, 8 times 196 and 4 times 225 is 900, 2 times 256 is 512. <br> Once you put that we?re gonna go through and basically add all of these together. So when you do that you get 7,847 as the total. <br> So the range, this one is quite actually easy. When we are looking to finding the range, you just looking at the highest score and the lowest score here. So the highest score take away the lowest score, 16 take away 7, and that giving you 9 as the range. <br> Alright! For the --inter quarter-- range we?ve got a little bit of figuring out to do in order to figure out which scores we?re looking at in our kilometer frequency column. So if we have 57 data items, the median, so let?s do a little bit of figuring out here. The median is going to be the 29th score. So what that means is we?ve got score number 29 here, that?s the median. We have 28 scores in the lower half and 28 scores in the upper half. SO 28 and 28 they?re both even numbers. We?re going to half of 28 is 14, so the first quartile is gonna be between the 14th and the 15th score. So we?re doing the same thing we did here, 28 plus 1 which is 29 divide that by 2 we get 14.5th score is going to be at low value here. <br> Now we can use the same theory in the upper half. We are looking at finding basically the 14.5th score from 29 alright. So 28 plus 1 is 29 divide that by 2 we?re looking at the 14.5th score from the median. So if we add 14.5 to 29 we end up getting we?re looking at 43.5th score. So you are looking at 43rd and 44th score. <br> Okay so, Q1 is gonna be the 14.5th score and Q3 is gonna be the 43.5th score. So let?s have a look Q1 easy let?s started to start 14.5 so we got up to 13 there, 14 and 15 are gonna be in there. So Q1, is going to be 10 . Q3 we?re looking at the 43.5th so 43 is up to here, number 44 is in there so Q3 is actually gonna be 13 plus 14 divided by 2 which is basically 13.5. So the interquartile range is going to basically be Q3 minus Q1, 13.5 take away 10 which is 3.5. <br> The last thing we need to do is figure out the standard deviation, Now in order to do the standard deviation we first of all need the mean. So the mean is sum of scores divided by the number of scores. So from the table here the sum of scores is 655, we need to divide that by 57 because that?s how many scores we?ve got. So when we do that we got 11.4912281 And now we can figure out the standard deviation. It is the square root of the sum of the overall score so the frequency times the score squared, so it is up here, F or f squared. We?re gonna divide that by number of scores and then take that away from the main squared. <br> So here while looking at from our table, 7847 we?re gonna divide that by 57 and then we?re going to just before we?re gonna take away 11.4912281 squared. Alright! So 7847 divided by 57 gives us 137.6667. Let?s find the main squared 11.4912281 square that. That?s 132.0483 <br> Okay so there?s couple of steps here 137.6667 take away 132.0483 looking at finding the square root of 5.6184 and when we do that the standard deviation of the mean, 2.37 <br> Okay so you can finish off by just writing a sentence to state your answer . The range is 9. The interquartile range is 3.5 and the standard deviation is 2.37 for this data set. All done. So once you do all work on the table you really don?t have much that to do.