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Algebra 1 : How to find range

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Example Question #11 : How To Find Range

In the field of hematology, a patient's blood oxygen content is considered "stable" if the readings taken over a period of 24 hours have a range no larger than 4.5. A day's readings for a patient are below. Is this patient's blood oxygen content stable?

98.5, 99.2, 95.1, 94.9, 97.8, 98.8, 99.1, 97.5

Possible Answers:

Yes, the range is less than 4.5.

No, the range is more than 4.5.

No, the range is less than 4.5.

There is not enough data to answer the question.

Yes, the range is more than 4.5.

Correct answer:

Yes, the range is less than 4.5.

Explanation:

To compute range, we must first identify the least and greatest values in a data set. The easiest way to do this is to order the set:

$98.5, 99.2, 95.1, 94.9, 97.8, 98.8, 99.1, 97.5\rightarrow$ $\bf 94.9,$ 95.1, 97.5, 97.8, 98.5, 98.8, 99.1, $\bf99.2$

Range is found by the equation $x_{max}-x_{min}$ , or the maximum value in the set minus the minimum value.

Thus, our range is 99.2-94.9 = 4.3 .

Since $4.3\leq 4.5$ , the blood oxygen level is considered stable.

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Example Question #11 : How To Find Range

An ecosystem is considered to have "mild" climate if the range of its temperatures over a calendar year is less than $15^{\circ}$ , "moderate" climate if the range is between $15^{\circ} C$ and $20^{\circ} C$ , and "severe" if the range is more than $20^{\circ} C$ .

Average monthly temperatures in Celsius for a sample climate are given below (December through November). What statement can be made about the climate of this sample?

9, 12, 17, 20, 18, 23, 25, 26, 25, 22, 16, 14

Possible Answers:

The climate is both moderate and severe.

The climate is mild.

The climate is severe.

There is not enough data to answer the question.

The climate of the sample is moderate.

Correct answer:

The climate of the sample is moderate.

Explanation:

In this problem, finding the range of the sample is as simple as subtracting the lowest temperature value, $9^{\circ}C$ , from the highest, $26^{\circ}C$ .

$range = x_{max}-x_{min} = 26^{\circ}-9^{\circ} = 17^{\circ}$

Since $17^{\circ} C$ is in the range of $15^\circ \leq x \leq20^\circ$ which is the range for "moderate" climate, we may say that the sample shows a moderate climate.

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Example Question #11 : How To Find Range

$\small 10, 23, 4, 10, 22, 3, 5$

Using the data above, calculate the range.

Possible Answers:

$\small 20$

$\small 23$

$\small 2$

$\small 10$

Correct answer:

$\small 20$

Explanation:

The range is found by finding the difference between the highest and lowest values in a given set. In this set the highest number is $\small 23$ and the lowest is $\small 3$ . Using this data, simply subtract three from twenty-three. Our answer is $\small 20$ .

$\small 10, {\color{Red} 23}, 4, 10, 22, {\color{Red} 3}, 5$

23-3=20

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Example Question #11 : How To Find Range

$\small 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 , 100$

Using the data above, find the range.

Possible Answers:

$\small 10$

$\small 99$

$\small 124$

Correct answer:

$\small 99$

Explanation:

To find the range of a data set, we must first identify the highest value given: $\small 100.$

Next, we identify the lowest value given, $\small 1$ .

Now we must find the interval between these two numbers, $\small 100-1 = 99$ .

This is our range. Note that the data piece value of $\small 100$ , is considered an outlier, meaning it is dramatically different than the rest of the data values. When an outlier is present, expect the range to be very large compared to the rest of the data values.

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Example Question #591 : Statistics And Probability

$\small 23, 42, 53, 22, 55, 12, 56$

Using the data above, find the range.

Possible Answers:

$\small 23$

$\small 15$

$\small 45$

$\small 44.$

Correct answer:

$\small 44.$

Explanation:

The first step is to find the highest value given in the data set, in this case: $\small 56.$

Next, we find the lowest value, in this case: $\small 12$ .

The range is defined as the difference between the highest and lowest values.

Thus, the range for this set of data is $\small 56 - 12 = 44$ .

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Example Question #592 : Statistics And Probability

$\small 6,6,9,10,15,16,20,30,48$

Using the data set above, find the range and mode.

Possible Answers:

$\small range = 42, mode = 8$

$\small range = 32, mode = 6$

$\small range = 42, mode = 6$

$\small range = 40, mode = 8$

Correct answer:

$\small range = 42, mode = 6$

Explanation:

The range is defined as the difference between the highest and lowest value in the data set.

For this data set,

$\small 48 - 6 = 42,$ thus $\small 42$ is the range.

The mode is the value that appears the most amount of times. In this set every value appears once, except the number six, which apperas twice. The mode is $\small 6$ .

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Example Question #593 : Statistics And Probability

$\small \small 390,23,8940,283,4,4,4,4,4,4,4,4,14,134,1$

Using the data, find the range and the mean.

Possible Answers:

$\small mean= \frac{991}{15}, range = 3890$

$\small mean= \frac{9961}{15}, range = 95$

$\small mean= \frac{9817}{15} , range = 8939$

$\small mean= \frac{9961}{15}, range = 45$

Correct answer:

$\small mean= \frac{9817}{15} , range = 8939$

Explanation:

To find the mean of a data set, we add all of the data values and divide the sum by the number of data values in the set. In this set there are fifteen data values.

$\small \small \frac{390+23+8940+283+4+4+4+4+4+4+4+4+14+134+1}{15} = \frac{9817}{15}$ , this is our mean.

The range is simply the interval between the biggest and smallest numbers,

$\small 8940-1 = 8939$ . This is our range.

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Example Question #594 : Statistics And Probability

$\small 34,2,39,30,45,33$

Using the data above, find the range and the mode, if any.

Possible Answers:

$\small mode = none, range= none$

$\small mode = none, range= 43$

$\small mode = 43, range= none$

$\small mode = none, range= 40$

Correct answer:

$\small mode = none, range= 43$

Explanation:

When provided with the data:

$\small 34,2,39,30,45,33$ ,

the easiest thing to obtain first is the mode.

Do any of these numbers appear more than once? The answer is no. All of these numbers only appear once, meaning that there is no mode in this set.

Next, we use the highest and lowest numbers to find the range.

In this set, these numbers are:

$\small 45-2 = 43$ ,

thus this is the range.

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Example Question #595 : Statistics And Probability

What is the range of the following number set?

2,4,5,1,10,11,3

Possible Answers:

Correct answer:

Explanation:

We define range as the difference between the lowest and highest numbers in a given number set.

In our set 2,4,5,1,10,11,3 , the highest number is and the lowest number is .

Therefore, the range is 11-1=10 .

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Example Question #596 : Statistics And Probability

What is the range of the following number set?

0,1,5,3,7,6,2,8,9,17,12

Possible Answers:

Correct answer:

Explanation:

We define range as the difference between the lowest and highest numbers in a given number set.

In our set 0,1,5,3,7,6,2,8,9,17,12 , the highest number is and the lowest number is .

Therefore, the range is 17-0=17 .

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Algebra 1 : How to find range

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #11 : How To Find Range

Example Question #11 : How To Find Range

Example Question #11 : How To Find Range

Example Question #11 : How To Find Range

Example Question #591 : Statistics And Probability

Example Question #592 : Statistics And Probability

Example Question #593 : Statistics And Probability

Example Question #594 : Statistics And Probability

Example Question #595 : Statistics And Probability

Example Question #596 : Statistics And Probability

All Algebra 1 Resources

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