The numbers in the "stem" of this display represent tens digits of the test scores, and the numbers in the "leaves" represent the units digits. This stem-and-leaf display represents twenty scores.

The interquartile range is the difference of the third and first quartiles.

The third quartile is the median of the upper half, or the upper ten scores. This is the arithmetic mean of the fifth- and sixth-highest scores. These scores are 73 and 69, so the mean is \(\displaystyle \left (73 +69 \right )\div 2 = 71\). 

The first quartile is the median of the lower half, or the lower ten scores. This is the arithmetic mean of the fifth- and sixth-lowest scores. Both of these scores are the same, however - 57.

The interquartile range is therefore the difference of these numbers: \(\displaystyle 71-57 = 14\)

The midrange of a data set is the arithmetic mean of its greatest element and least element. Here, those elements are \(\displaystyle 9\) and \(\displaystyle -10\), so we can find the midrange as follows:

\(\displaystyle \left [9 + (-10) \right ]\div 2 = -1\div 2 = -0.5\)

The range of a set of numbers is the difference between the highest number and the lowest number in the set.

The range of set 1 is:

 \(\displaystyle 27-(-2)=29\)

The range of the second set, ignoring the value of m is: 

\(\displaystyle 23-(-3)=26\)

We need to either subtract 3 from the lowest number in set Set 2 or add 3 to the highest number in Set 2 to get the value of m such that the range of both sets are equal.

\(\displaystyle m=(-3)-3=-6 \rightarrow range =23-(-6)=29\) 

or

\(\displaystyle m=23+3=26 \rightarrow range = 26-(-3)=29\) 

The range of a set of data is the difference between its highest value and its lowest value, as this describes the range of values spanned by the set. A quick way to calculate the range is to locate the lowest value in the set and subtract it from the highest value, but let's arrange the set in increasing order to visualize the problem first:

\(\displaystyle (9, 12, 14, 15, 16, 17, 21, 22, 23, 24, 27)\)

Now we can see that the lowest value in the set is 9, and the highest value in the set is 27, so the range of the set is:

\(\displaystyle 27 - 9 = 18\)

The range of a set of data is the difference between its smallest and greatest values. We can first look through the set for the greatest value, which we can see is 53. We then look through the set for the smallest value, which we can see is 28. The range of the set is then:

\(\displaystyle 53-28=25\)

To find the range, simply subract the smallest number from the largest. Therefore:

\(\displaystyle 8-2=6\)

To find range, subtract the smallest number from the largest number. Thus,

\(\displaystyle \textup{range}=28-4=24\)

To find the range, you m ust subtract the smallest number from the largest. Thus,

\(\displaystyle 11-1=10\)

Find the range of the following data set:

\(\displaystyle 89,34,117,42,367,2,989,463,865\)

Range is as simple as finding the diffference between the largest and smallest terms in a set. So, let's find our largest and smallest terms.

Largest: 989

Smallest: 2

Next, let's calculate the range:

\(\displaystyle r=989-2=987\)

So our answer should be 987

The midrange of a set is the arithmetic mean of the greatest and least values, which here are \(\displaystyle A\) and \(\displaystyle F\). This makes the midrange \(\displaystyle \frac{A+F}{2}\).