63 94 64 72 87 91 78 81 52 60 73 85 50 58 88 72 64 55 62 77...

63 94 64 72 87 91 78 81 52 60 73 85 50 58 88 72 64 55 62 77 88 65 77 85 43 61 86 76 71 73 79 64 Diagram 1 a) Based on the data above, complete the Table 1 below. Marks Frequency Class Boundaries Midpoint 30-39 0 29.9-39.9 34.5 40-49 2 39.9-49.9 44.5 50-59 5 49.9-59.9 54.5 60-69 10 59.9-69.9 64.5 70-79 12 69.9-79.9 74.5 80-89 8 79.5-89.9 84.5 90-99 3 89.9-99.5 94.5 Table 1

Transcript

00:01 There is given a table and for this question we have to calculate the mean, variance and the standard division.

00:10 So mean, median, variance and standard division.

00:13 Okay, here we go.

00:14 Let's first of all start with the mean value.

00:17 So we have the boundaries, i mean the interval.

00:21 We need to get the midpoint.

00:22 So the midpoint was also given in the table.

00:24 So in order to get the mean, which is the midpoint times the frequency and divided by the total frequency.

00:31 So this is 0 times 34 .5 plus 1, sorry, this is 2 times 44 .5 up to the last point which is 3 times 94 .5 and this is divided by the total frequency.

00:49 So the total frequency 7172937 which is 40.

00:54 Let's get this value.

00:56 So this is 2 times 44 .5 and plus the next one here, sorry, we don't need, actually, we don't need the parentheses.

01:10 The next one is 5 times 44 .5 and the next one which is 10 times, this is 54 .5 and plus the next one 12 times 64 .5 and plus sorry, this is 5 times, so this is 2 times, sorry, let me check, 44 .5, 5 times 54.

01:37 Okay, so this should have been the 54 on the calculator and this one is 64 and the last one i wrote here should have been the 74 and after 12 we have the 8, so this is 8 times which is 84 .5 and plus the last one which is 3 times, this is 94 .5.

02:10 So what about their sum? their sum is 2860 and divided by 40.

02:15 So this is, i'm gonna divide this number by 40.

02:18 So the mean value which is 40 here, sorry, 2860 and divided by 40 which is 71 .5.

02:27 This is the mean score here.

02:30 And what about the median score? so for the median score, which is the total frequency minus 1 and divided by 2 term, so this is 40, so 40 plus 1 divided by 2 which would be 20 .5.

02:47 So 20 .5 term from the beginning, 2, 5, 17.

02:52 So it is in the interval 70 and 79.

02:55 So we can say the median, median for this question, which is between 70 and 79.

03:02 And what about the variance? for the variance, this is the sum of the middle term minus the mean squared and divided by the total frequency...

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