Measures of Spread and Sushi

If the buzz about the new sushi restaurant has only 3.5 stars on Yelp, should you go?

 

It depends on the measure of spread.  First look at the range, which is the difference between the highest and lowest rating.  Most likely, in this example, the range would be the difference between one star and five stars.  You might state that the range is between one and five, and therefore the range is four.

 

The standard deviation is the measure of spread of data around the mean, which since last week (and likely since third grade) you know is the average of the data.  Is the data clustered around the mean?  Then you may be able to figure out that most people find the restaurant pretty average, and thus no reason for the hype.

 

The standard deviation is the average distance from the mean of the average score. Luckily, you will not have to do this by hand, but it is good to know that in all surveys, at least 75% of responses will fall within the mean plus two standard deviations.

 

If you take a quick look at the sushi reviews and see that most people gave the restaurant four and five stars, but a couple of one star reviews fell outside the standard deviation, you may be more willing to visit since these one star reviews lowered the average, which is exactly what they intended!

 

The percentILE (not percentAGE) shows the percent of distribution equal to or below a given number.  Continuing with the sushi example, if you wanted to research ten or twenty other sushi restaurants to determine how many stars each received, you may find that your choice is in the 85th percentile.  This means that 85% of other sushi restaurants rated the same or below the restaurant you are considering.

 

The last measure of spread to examine for descriptive statistics is the interquartile range, which is the difference between the 25th and 75th percentile.  It is looking at 50% of responses, those in the middle, and asking, what do those people think?  It is similar to the mode in that the mode is the data the shows up most often, and the interquartile range is the middle section of data, where much of it falls in the measure of dispersion.

 

By the time you have considered your range, standard deviation, percentile, and interquartile range in reviewing sushi restaurants, your date may have headed up to the McDonalds, deciding that choosing a sushi restaurant was the least of the evening’s obstacles.  Use your statistical powers sparingly.

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