3.3 Measures Of Spread

If each of the numbers in the set is decreased by 11, the new set of numbers would be:
-3 (8 minus 11)
0 (11 minus 11)
8 (19 minus 11)
19 (30 minus 11)
To find the mean of this new set, we add up all the numbers and divide by the total count. In this case, the sum of the new set is 24, and since there are 4 numbers, the mean would be 24 divided by 4, which is 6.

The interquartile range is a measure of the spread or variability of a dataset. It is calculated by finding the difference between the upper quartile and the lower quartile. In this case, the lower quartile is the median of the first four numbers (56 and 66) and the upper quartile is the median of the last four numbers (103 and 109). So, the interquartile range is 109 - 56 = 45.

If one of the numbers in the set is increased by 10, the new sum of the set would be the original sum plus 10. Since the mean is calculated by dividing the sum by the number of values, the new mean would be the new sum divided by 5 (since there are still 5 numbers in the set). Therefore, the new mean would be (original sum + 10) / 5, which simplifies to (130 + 10) / 5 = 140 / 5 = 28.

The standard deviation is a measure of how spread out the data is from the mean. To calculate the standard deviation, we first find the mean of the data set, which is the sum of all the numbers divided by the total number of numbers. In this case, the mean is 81.9. Then, we subtract the mean from each data point, square the result, and sum all the squared differences. Next, we divide the sum by the total number of numbers minus 1, and finally, take the square root of the result. In this case, the standard deviation is 27.5.

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