1. Answer, explain and show work for the following question. a. For the numbers

Question

1. Answer, explain and show work for the following question.

a. For the numbers 1, 3, 4, 6, and 12:

Find the value (v) for which (X-v)2 is minimized.

Find the value (v) for which |x-v| is minimized.

b. Here is a simple data set: 150, 250, 175, 225, 700.   Calculate these statistics: the mean, median, standard deviation, range, and IQR ?   NOW, assume 700 was a data entry error and should be 300. Which statistics change? NOW, assume 700 is simply “bad data” and is dropped (now have only 4 data points). What changes?

Explanation / Answer

a)

We need to find v such that:

S = (v-1)2 + (v-3)2 + (v-4)2 + (v-6)2 + (v-12)2 is minimised

= 5v2 - 52v + 206

This is minimum when dS / dv = 0

i.e 10v - 52 = 0

v = 5.2

Now,

| v - 1 | + | v - 3 | + | v - 4 | + | v - 6 | + | v - 12 | is to be minimised.

Cases have to be taken where, v < 1; 1 < V < 3; 3 < v < 4; 4 < v < 6 ; 6 < v < 12 and v > 12

and the condition has to be checked for each value.

The value of v obtained satisfying the relation is v = 4

b)

The values are tabulated as shown

Hope this helps.

Data 150 150 150 250 250 250 175 175 175 225 225 225 700 300 Mean 300 220 200 Median 225 225 200 Std.Dev 227.0738 59.68668 45.6435465 Range 550 150 100 3rd quartile 250 250 231.25 1st quartile 175 175 168.75 IQR 75 75 62.5

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