# Statistical Range

Hi, and welcome to this video on Range! Range has two different definitions in math: the outputs of a function, or the difference between the highest and lowest values in a set of numbers. In this video, we will be talking about the second definition.

Range is one of four important values used in basic statistics. The other three are mean, median, and mode. Range tells you how big the spread of values is, meaning how far apart your largest and smallest values are. This is helpful in knowing how accurate your results are. For example, if your teacher gives the class a test and the highest grade is a 100, while the lowest grade is a 12, the range would be 88, which is pretty large for a test with a max score of 100.

The range is useful for knowing the accuracy of results, but usually can’t be used alone. It’s most useful when combined with one of the other three values. In our test example, knowing that there is such a large range could mean that the students scored all over the place: some really high and some really low, which would tell the teacher that he or she didn’t explain the information in a way that everyone could understand. But the teacher could get the same range of scores if everyone in the class got an A on the test but one person failed with a 12. The one person with a 12 is called an outlier, because he or she is not part of the normal grades for the class.

This is why knowing one of the other important values, especially the mean, is useful in interpreting the data. A low mean, or one in the middle, would give us the first conclusion, that the teacher could have explained things better in order for the whole class to understand. A high mean would give us the second conclusion, that most of the class did really well and understood the concept with a couple of outliers who may need some one-on-one help, but the teacher is able to move on to the next lesson.

The range for a set of data is found by subtracting the smallest value from the largest value. Let’s take a look at a few examples.

What is the range of this set of data?

{2, 13, 21, 19, 43, 4, 7, and 16}

Remember, for range all we need to know is the highest and lowest values. The highest value in this set is 43 and the lowest value is 2.

$$43 – 2 = 41$$

Our range is 41, which is fairly large for this data set.

Let’s look at another one.

Find the range of the following set of data:

{392, 184, 139, 256, 157, 237, and 376}

Our largest value for this set is 392 and our smallest value is 139, so our range is $$392 – 139$$, which is 253. This is a very large range of data.

Let’s try one more example, this time applying it to grades like we did earlier.

A teacher gave five students a test over Mean, Median, Mode, and Range. The scores on the test were: 100, 88, 98, 97, and 83. What is the range of the test grades?

The range is $$100 – 83$$ which equals 17. The range is low and the test grades are high, so everyone did really well on the test!

I hope this review of statistical range was helpful. Thanks for watching and happy studying!

## Practice Questions

Question #1:

Find the range of the following set of data:

11, 64, 39, 4, 42, 28, 7, 9

2

55

60

57

To find the range, identify the highest value and the lowest value in the data set. The highest value is 64, and the lowest value is 4. Since the range is equal to the difference between these two numbers, subtract to find the range. $$64-4=60$$, so the range is equal to 60. Therefore, answer C is correct.

Question #2:

Find the range of the following set of data:

564, 329, 463, 442, 570, 389, 451

241

113

250

235

First, identify the highest value and the lowest value in the data set. The highest value is 570, and the lowest value is 329. Since the range is equal to the difference between these two numbers, subtract to find the range. $$570-329=241$$, so the range is equal to 241. Therefore, answer A is correct.

Question #3:

Find the range of the following set of data:

4.8, 2.25, 9.8, 7.5, 12.50. 11.2

6.4

10.25

9.8

2.25

First, identify the highest value and the lowest value in the data set. The highest value is 12.50, and the lowest value is 2.25. Since the range is equal to the difference between these two numbers, subtract to find the range. $$12.50-2.25=10.25$$, so the range is equal to 10.25. Therefore, answer B is correct.

Question #4:

Rose took seven math tests over the course of the last grading period. Her scores are shown below. What is the statistical range of these scores?

90, 72, 85, 89, 92, 95, 78

12%

18%

20%

23%

First, identify the highest value and the lowest value in the data set. The highest value is 95 percent, and the lowest value is 72 percent. Since the range is equal to the difference between these two numbers, subtract to find the range. $$95-72=23$$, so the range is equal to 23 percent. Therefore, answer D is correct.

Question #5:

The forecasted high temperatures in Philadelphia, Pennsylvania for the next nine days are listed below. What is the range of these temperatures?

72, 66, 82, 77, 84, 72, 66, 63, 66

21 degrees

6 degrees

18 degrees

14 degrees

First, identify the highest value and the lowest value in the data set. The highest value is 84 degrees, and the lowest value is 63 degrees. Since the range is equal to the difference between these two numbers, subtract to find the range. $$84-63=21$$, so the range is equal to 21 degrees. Therefore, answer A is correct.