How to find range - SAT Math

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Question

Find the range.

\dpi{100} \small 9,6,1,6,5,9,8,3

Answer

First, arrange the numbers from highest to lowest, then subtract the highest number from the lowest number.

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Question

The median of a set of eleven consecutive odd integers is 39. What is the range of the set?

Answer

Let's represent the eleven integers as A, B, C, D, E, F, G, H, I, J, and K. Let's assume that if we lined them up from least to greatest, the set would be as follows:

A, B, C, D, E, F, G, H, I, J, K

The median in this set is the middle number. In this case, the middle number will always be F, because there are five numbers before it and five numbers after it.

We are told that the median is 39. Thus F = 39, and our set looks like this:

A, B, C, D, E, 39, G, H, I, J, K

Since we know that all the numbers are consecutive odd integers, the set must consist of the five odd numbers before 39 and the five odd numbers after 39. In other words, the set is this:

29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49

The question asks for the range of the set, which is the difference between the largest and smallest numbers. In this case, the range is 49 – 29 = 20.

The answer is 20.

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Question

Find the range of the following sequence:

1, 3, 4, 6, 11, 23

Answer

To find the range, subtract the smallest number from the largest number. In this case we get 23 - 1 = 22 so the range is 22.

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Question

What is the range of the data set below?

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

Answer

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

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Question

Find the range of the data set:

25, 83 , 51, 13, 37, 21, 52, 58

Answer

44 is the median of the data. 42.5 is the arithmetic mean. 13 is the minimum value. 83 is the maximum value.

To find the range, subtract the minimum value from the maximum value:

83 - 13 = 70

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Question

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?

Answer

We know that H = 2G = 4F, and G = 2F and that (F + G + H)/3=21. If we substitute each term with its F equivalent we get:

(F + 2F + 4F)/3 = 21

7F/3 = 21

7F = 63

F = 9

If we substitute F = 9 into H = 4F, we get H = 36.

The correct answer is 36.

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Question

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?

Answer

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.

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Question

You have the following data set:

.

What is the range of the data set?

Answer

The range can be obtained by subtracting the lowest number in the set from the highest number in the set.

The lowest number in the set is 2 and the highest number is 66.

Therefore, is the range of the data set.

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Question

The following numbers are selected from a set of data:

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

Answer

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 .

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Question

What is the range of the following data set?

Answer

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.

It can then be seen that the smallest fraction is and the largest fraction is .

Write the range formula and solve.

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Question

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

Answer

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.

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Question

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?

Answer

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

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:

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Question

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?

Answer

The total value of the tiles is

There are 100 tiles, so the mean value is

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Question

Find the range of the following set of numbers:

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

Answer

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,

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