How to find range - Algebra 1

Card 0 of 20

Question

$\left { 89, 98, 77, 92, 93 \right }$

Given the set of test scores, what is the range?

Answer

The range is the difference between the smallest number and the largest number. The smallest value is 77, and the largest is 98.

98 – 77 = 21

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Question

The range of the following data set is 18. What is a possible value for ?

$\left { 3, -5, 7, 7, 5, 10, x, 1, -2 \right }$

Answer

Arrange the known values in the set in numerical order: {–5, –2, 1, 3, 5, 7, 7, 10}. The range is the difference between the largest value and smallest value.

x must be either the largest or the smallest value in the set.

range = x – smallest value

18 = x – (–5)

18 = x + 5

13 = x

OR

range = largest value – x

18 = 10 – x

8 = –x

–8 = x

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Question

The above chart shows a specific week of work at an advertising firm. What is the range of the hourly rates of the workers?

Answer

The range is difference between the largest value and the smallest value.

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Question

What is the range of the set $\left { -2,6,13,25,-2,4,11\right }$ ?

Answer

The range is defined as the difference between the highest and lowest numbers in a set. Here, the highest number is and the lowest is .

Therefore, the range is

is the mode, is the mean, and 6 is the median.

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Question

A teacher is grading quizzes and recording the scores in her records. The scores are recorded as follows: 81, 91, 83, 88, 74, 98, 81, 94, 68, 92, 77, 79, 83, 91, 81, 84, 85, 81, 85, 79, 83, 81, 83.

What is the range?

Answer

The range of the statistics is simply the difference between the largest value and the smallest value.

The largest number in the set is 98, and the smallest number is 68.

Subtract to find the range:

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Question

We want to create a three digit code for a combination lock. Only digits from 0-9 are allowed and digits can be repeated. How many such codes can be generated?

Answer

The first position can be filled 10 ways and since repetition is allowed, the 2nd position can be filled in 10 ways and similarly the third position can be filled in 10 ways as well, giving us the correct answer of

$10^{3}$

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Question

Evaluate:

$C\binom{5}{3}$

Answer

This is a combination problem. All we need to solve this problem is the combination formula: $C\binom{n}{k}=\frac{n!}{k!(n-k)!}$

$C\binom{5}{3} = \frac{5!}{2!\times 3!}$

Now $5! = 5\times 4\times 3\times 2\times\times 1$

$3!= 3\times 2\times 1$

and $2! = 2\times 1$

Instead of finding answers for all of these factorials, notice that they have many of the same terms and can therefore be cancelled.

$\frac{5\times 4\times3\times2\times1}{3\times2\times1\times2\times1}=\frac{5\times4}{2}=5\times2=10$

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Question

You are given the following number set:

2, 8, 3, 6, 9, 10, 5

Find the range.

Answer

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

The lowest number in the number set is 2 while the highest number is 10. Therefore, the range is calculated as

So 8 is the range.

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Question

Find the range of the following set of numbers.

Answer

Subtract the lowest number (4) from the highest (52) to get 48.

$24, 4, {\color{Red}{52}}, 39, 23, 25, 48, 12, {\color{Red} 4}$

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Question

In the set of numbers, what is the range?

Answer

To determine the range of this data set, take the largest number and subtract it with the smallest number.

The largest number in the set is ten.

The smallest number in the set is .

Subtract both numbers.

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Question

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?

Answer

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:

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

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 .

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

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Question

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?

Answer

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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Question

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

Using the data above, calculate the range.

Answer

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 $\small 20$ .

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

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Question

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

Using the data above, find the range.

Answer

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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Question

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

Using the data above, find the range.

Answer

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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Question

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

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

Answer

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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Question

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

Using the data, find the range and the mean.

Answer

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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Question

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

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

Answer

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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Question

Consider the following set of numbers:

Find the range of the set.

Answer

To find the range of the set, subtract the smallest number in the set from the largest number in the set.

In this set the largest number is and the smallest number is .

Therefore, the difference or range is,

.

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Question

Consider the following set of numbers:

Find the range of the set.

Answer

To find the range of the set, subtract the smallest number in the set from the largest number in the set.

${\color{Blue} 61}, 65, 68, 71, 72, 72, 72, 74, 79, 82, 86, 88, {\color{Green} 88}$

The smallest number in the data set can be seen in blue, .

The largest number in the data set can be seen in green, .

Therefore, the difference or range becomes,

.

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