Question

AThe range and standard deviation of the data set below are 35 and 12.47 respectively 5, 24, 25, 26, 40 If the 26 is replaced with 39, how will this affect the range? How will this affect the standard deviation. Use your answers to explain why the standard deviation is preferable to the range as a measure of variation. reseemn deviation? You are late for work. You have two options for getting to work. You may take the bus which takes on average 4 minutes with a standard deviation of 12 minutes. Or you can cycle which takes on average 50 minutes with a standerd desviation of 2 minutes. Compare these two distributions You leave your house at 8.20 am and are supposed to start work at 9.00 am. Which option would you choose if you will be fired if you are even a few minutes late? Which option would you choose if you know that up to 15 minutes late is OK but after that there is trouble? Explain your thinking. acturing nrocess there is

Answer 1

Now the maximum value = 40

Minimum value = 5

The range is

Range = maximum - minimum = 40-5 = 35

Interpretation: The range remain same as maximum and minimum values are same.

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Following table shows the calculations for standard deviation:

	X	(X-mean)^2
	5	466.56
	24	6.76
	25	2.56
	39	153.76
	40	179.56
Total	133	809.2

Sample size n5 Sample sum: Σx 13 Sample mean: =133/5 n 26.6 Sample standard deviation: Σ(r-5 x -sqrt(809.2/(5-1)) n-1 -14.2232

Conclusion: Standard deviation has been changed as we changed one value but range remains same because maximum and minimum values are same as before. So standard deviation is preferable measure of variation.