Using SAS, make a random sample on Sales 2 distribution from the data in Figure

Question

Using SAS, make a random sample on Sales 2 distribution from the data in Figure 5.1. Using the software, determine six items from the data set for sampling purposes. Which specific values should be selected from the data set?

OBV Sales 1 Sales 2 Sales 3 Sales 4 1 23 1234 1 1 2 31 943 2 5 3 48 986 3 9 4 16 12 4 12 5 28 15 5 18 6 29 15 6 19 7 31 23 6 19 8 35 21 6 21 9 51 25 6 21 10 42 27 7 21 11 34 27 8 21 12 56 29 9 21 13 24 20 10 21 14 34 18 11 19 15 43 13 12 19 16 56 8 13 18 17 34 7 14 12 18 38 6 15 9 19 23 4 16 5 20 27 1 17 1

Explanation / Answer

The mean for grouped data, in which data has been tabulated by range and exact values are not known, is calculated in a similar manner. Because we don’t know the exact values for each case (we know, for instance, that 5 values fell into the range of 1–20 but not the specific values for those five cases), for the purposes of calculation we use the midpoint of the range as a stand-in for the specific values. Therefore, to calculate the mean, we first calculate this midpoint for each range and then multiply it by the frequency of values in the range. To calculate the midpoint for a range, add the first and last values in the range and divide by 2. For instance, for the 1–20 range, the midpoint is:

(1 + 20)/2 = 10.5

A mean calculated in this way is called a grouped mean. A grouped mean is not as precise as the mean calculated from the original data points, but it is often your only option if the original values are not available.

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