Critical Thinking. For Exercises 5–20, watch out for these lit...

Question

Critical Thinking. For Exercises 5–20, watch out for these little buggers. Each of these exercises involves some feature that is somewhat tricky. Find the (a) mean, (b) median, (c) mode, (d) midrange, and then answer the given question.

Smart Thermostats Listed below are selling prices (dollars) of smart thermostats tested by Consumer Reports magazine. If you decide to buy one of these smart thermostats, what statistic is most relevant, other than the measures of central tendency?

250 170 225 100 250 250 130 200 150 250 170 200 180 250

Accepted Answer

Hi everyone, let's take a look at this practice problem. This problem says the following are selling prices in dollars of wireless security cameras tested by a consumer review agency, and we're given the values of $240 160 dollars, $220.90 $240 240, 120, 190, 140, 240, 160, 190, 170, and 240. If you were selecting a security camera, what other statistics, besides measures of central tendency would be useful in decision making? We have 4 possible choices as our answers. For choice A, we have the number of data points. For choice B, we have the range. For choice C, we have coefficient of variation, and for choice D, we have sample size. Now, this question is asking us what statistic, other than the measures of essential tendency, would be useful in decision making in selecting a security camera. Now, our central tendencies, uh, measures, which are our mean, median, and mode, they don't really give us any information about price variation, and that would be something that would be important in our decision making process. So, we're gonna be looking for quantities that tell us about the price variation of our data. So one quantity that will tell us about the variation in our prices here is going to be the range, and recall that the range is equal to our maximum value minus our minimum value. So, in this case, it's going to be 240 minus 90, which is equal to 150. So here we see a high range. Which indicates a wide variation in prices, meaning that prices can differ significantly between models. Now, the other um quantity that gives us variation is our coefficient of variation, and this measures relative variability, but it is more complex and less intuitive than the range in this decision making context. So, the range is going to be a better quantity to look at than the coefficient of variation. And if we look at our other two possible answer choices, the number of data points and sample size, the number of data points just tells us how many cameras were tested and doesn't tell us anything about price variation, and seemingly, the same can be said for sample size. So, based on this information, we see that the correct answer choice corresponds to answer choice B, which is the range. So, I hope that this explanation has been useful, and I'll see you in the next video.

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Key Concepts

Measures of Central Tendency

Variability

Contextual Relevance of Statistics

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