43 45 53 56 56 57 58 66 67 73 74 79 80 80 81 81 81 82 83 83...

43 45 53 56 56 57 58 66 67 73 74 79 80 80 81 81 81 82 83 83 84 88 89 91 91 92 92 97 99 99 100 100 101 102 102 102 103 104 107 108 109 113 114 118 121 123 126 128 137 138 139 144 145 147 156 162 174 178 179 184 191 198 211 214 243 249 329 380 403 Which numerical summary would you choose for these data? Calculate your chosen summary. How does it reflect the skewness of the distribution?

Transcript

00:01 All right, so for this problem, to begin, for part a, we're asked for the measures of central tendency.

00:05 One is going to be our sample mean value, which we find by taking the sum of all of the individual data points, and dividing by the number of data points.

00:19 I'll note that we have 80 data points here.

00:23 So when we calculate our mean value, just giving a few example values, we'd have 116 plus 100, plus 127, plus don't.

00:34 Up until the 80th value in this accounting of it would be 799.

00:39 I'm going top left to bottom right there for x1 through x80.

00:43 So when we add all of those up and divide by 80, we'll get a result of 331 .5125, roughly.

00:53 The other measure of central tendency would be the median.

00:58 So i'll note that if we are assuming now, this is a different sort of indexing of the data points, but if we're assuming that the data is ordered, then the median is going to be the average of the 40th data point and the 41st data point.

01:16 Plugging in those values, we'd actually have that both of them are 119 when we ordered the data.

01:24 So we have that the median value is 119.

01:26 That's significantly smaller than x bar.

01:29 So that means that this is a heavily skewed data set, which means that the median is going to be the most appropriate value for the central tendency.

01:40 And then related to that, our best estimate of the measure of variation then, because this is such a skewed distribution, would be to find the interquartile range, which is the third quartile minus the first quartile.

01:57 The third quartile is going to be the average of the 60th data point when we put everything in order...

Question

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