SAT Math - How to find range

What is the range of the following data set?

$\left(\frac{5}{9},\frac{2}{3}, \frac{3}{5}\right)$

$\frac{1}{9}$

$-\frac{2}{45}$

$\frac{1}{15}$

$\frac{2}{9}$

$\frac{1}{2}$

Explanation

Determine the smallest and largest fractions by rewriting all the fractions to a similar denominator.

Multiply all three denominators together to get the least common denominator, and multiply the numerators by what was multiplied by the denominator to obtain the new numerators.

$(\frac{5}{9},\frac{2}{3}, \frac{3}{5})=(\frac{75}{135},\frac{90}{135}, \frac{81}{135})$

It can then be seen that the smallest fraction is $\frac{5}{9}$ and the largest fraction is $\frac{2}{3}$ .

Write the range formula and solve.

$\textup{Range}= \textup{Largest} -\textup{Smallest}$

$\textup{Range}=\frac{2}{3}-\frac{5}{9}= \frac{6}{9}-\frac{5}{9}=\frac{1}{9}$

Mrs. Jung gave a geometry test to her 15 students. The scores were . What is the range of the test scores?

Explanation

The range of scores is from 75 to 100, which is a range of 25 points.

You take the highest score and subtract the lowest score from it.

The highest score is 100 and the lowest score is 75 therefore the range is as follows.

$\R=H-L \R=100-75 \R=25$

A set of numbers consists of eleven consecutive even integers. If the median of the set is 62, what is the range of the set?

Explanation

We don't know what the numbers are yet, so let's just call them a1, a2, a3, a4....a11. Let's assume a1 is the smallest, and a11 is the greatest.

If we were going to find the median of our set, we would need to line them all up, from least to greatest.

a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11

The median is the middle number, which in this case about be a6, because there are five numbers before it and five numbers after it.

We know that the median is 62, so that means that there must be five numbers before 62 and five numbers after. Because the numbers are all consecutive even integers, the set must look like this:

52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72

To find the range of this set, we must find the difference between the largest and smallest numbers. The largest is 72, and the smallest is 52, so the range is 72 - 52 = 20.

The answer is 20.

What is the range of the data set below?

103, 132, 241, 251, 623, 174, 132, 170, 843, 375, 120, 641, 384, 222, 833

103

833

740

473

545

Explanation

The range of a set of data is found by subtracting the smallest item from the largest. In this case, 843 - 103 = 740.

The following numbers are selected from a set of data:

Which of the following could NOT be the range of the data set?

Explanation

The range of the data is the difference between the largest number and the smallest number. The range of the given data is ; therefore, the range of the entire data set must be equal to or greater than . So, it could not be .

Find the range of the following set of numbers:

1,5,14,17,22,23,23

Explanation

To find range of any set of data, simply subtract the smallest number from the largest number. It is easiest if you order the numbers first. Thus,

Adam is comparing the prices of granola at different grocery stores in town. So far, these are the prices he's found:

If the average of these prices is then what is the range of all the prices?

Explanation

First, we want to solve for x. Since we know the average of all the prices is $1.90, then we can say

$\frac{2+2.5+1.75+2+x+1.7}{6}=1.9$

Now, we can find the range of the prices. The range is represented by the highest value minus the lowest value in any set. With that in mind, our range is given by:

A word game comprises 100 square tiles, each of which has a letter and a numeric value. Sixty of the tiles have value 1 each; twenty tiles have value 2 each; twelve of the tiles have value 4 each; four tiles have value 8 each; and two tiles have value 10 each. There are also two blank tiles with zero value.

What is the mean of the values of the tiles?

None of the other responses is correct.

Explanation

The total value of the tiles is

$60 \times 1 + 20 \times 2 + 12 \times 4 + 4 \times 8 + 2 \times 10 + 2 \times 0$

There are 100 tiles, so the mean value is $\frac{200}{100 } = 2$

F, G, H are the only three numbers in a sequence in which each number is twice the number before it. The three number have an arithmetic mean of 21. What is the value of H?