Is the difference between the highest and lowest numbers in a measurement range.

The Range is the difference between the lowest and highest values.

Inhaltsverzeichnis Show

The Range Can Be Misleading
Range of a Function
Some Limitations of Range
Practical Utility of Range
What is the difference between the highest and lowest numbers in the range?
Is the difference between the highest and lowest numbers in a measurement range quizlet?
Which is difference between the highest and the lowest measurement?
Is the difference between the highest and lowest numbers in a measurement signal?

Example: In {4, 6, 9, 3, 7} the lowest value is 3, and the highest is 9.

So the range is 9 − 3 = 6.

It is that simple!

But perhaps too simple ...

The Range Can Be Misleading

The range can sometimes be misleading when there are extremely high or low values.

Example: In {8, 11, 5, 9, 7, 6, 3616}:

the lowest value is 5,
and the highest is 3616,

So the range is 3616 − 5 = 3611.

The single value of 3616 makes the range large, but most values are around 10.

So we may be better off using Interquartile Range or Standard Deviation.

Range of a Function

Range can also mean all the output values of a function, see Domain, Range and Codomain.

696, 740, 1468, 1469, 2159, 2160, 3064, 3065, 3798, 3799

In statistics, range is defined simply as the difference between the maximum and minimum observations. It is intuitively obvious why we define range in statistics this way - range should suggest how diversely spread out the values are, and by computing the difference between the maximum and minimum values, we can get an estimate of the spread of the data.

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For example, suppose an experiment involves finding out the weight of lab rats and the values in grams are 320, 367, 423, 471 and 480. In this case, the range is simply computed as 480-320 = 160 grams.

Some Limitations of Range

Range is quite a useful indication of how spread out the data is, but it has some serious limitations. This is because sometimes data can have outliers that are widely off the other data points. In these cases, the range might not give a true indication of the spread of data.

For example, in our previous case, consider a small baby rat added to the data set that weighs only 50 grams. Now the range is computed as 480-50 = 430 grams, which looks like a false indication of the dispersion of data.

This limitation of range is to be expected primarily because range is computed taking only two data points into consideration. Thus it cannot give a very good estimate of how the overall data behaves.

Practical Utility of Range

In a lot of cases, however, data is closely clustered and if the number of observations is very large, then it can give a good sense of data distribution. For example, consider a huge survey of the IQ levels of university students consisting of 10,000 students from different backgrounds. In this case, the range can be a useful tool to measure the dispersion of IQ values among university students.

Sometimes, we define range in such a way so as to eliminate the outliers and extreme points in the data set. For example, the inter-quartile range in statistics is defined as the difference between the third and first quartiles. You can immediately see how this new definition of range is more robust than the previous one. Here the outliers will not matter and this definition takes the whole distribution of data into consideration and not just the maximum and minimum values.

It should be pointed out that in spite of several limitations, the range can be a useful indication for many cases. As a student of statistics you should understand what kinds of data are best suited to be defined based on range. If there are too many outliers, it may not be a good idea. But range gives a quick and easy to estimate indication about the spread of data.

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Mean, Median, Mode, and Range

Three types of averages can be used to describe a data set.

Averages

The mean of a data set is the sum of the values divided by the number of values.

The median of a data set is the middle value when the values are written in numerical order. If a data set has an even number of values, the median is the mean of the two middle values.

The mode of a data set is the value that occurs most often. A data set can have no mode, one mode, or more than one mode.

The range of a data set is the difference between the largest and smallest values in the set.

Math In Real Life

Example

A marine biologist records the locations of deep sea jellies in relation to the ocean surface. Jellies are found at -2,278 feet, -1,875 feet, -3,210 feet, -2,755 feet, -2,407 feet, and -2,901 feet.

What is the average location of a deep sea jelly?

Find the Mean

To find the mean of the 6 locations of the deep sea jellies in the problem above, divide the sum of the locations by 6.

The mean location in relation to the ocean surface is -2571 ft.

Guided Practice (Ask your tutor for help.)

1) Find the mean of the data.

2) Find the mean of the data.

Finding Median, Mode, and Range

Find the median, mode(s), and range of the movie prices below.

$7.20, $13.25, $14.94, $16.56, $18.74, $19.99, $19.99, $29.49

Median

The data set has an even number of prices, so the median is the mean of the two middle values, $16.56 and $18.74.

Mode

The price that occurs most often is $19.99. This is the mode.

Range

The range of a data set is the difference of the greatest value and the least value.

Range = $29.49-$7.20=$22.29

Choosing a Representative Average

Groups A and B try a new ice cream flavor and rate it on a scale of 1 to 10 as shown. Which average best represents each group?

Solution

The mean, median, and mode are very close. So each average is a fair representation of the ratings as a group.

The mean is higher than all but 3 ratings. The mode is equal to the lowest rating. So, mean and mode are not good choices. The median best represents the ratings.

Guided Practice (Ask your tutor for help.)

3) Find the Error
Describe and correct the error in the solution.

4) Use the data set 6, 12, 4, 15, 10, 6, 2, 9 to complete the statement using mean, median, mode, or range.

a. The _?_ is 8.

b. The _?_ is 6.

c. The _?_ is 13.

5) Jocelyn is training to run in a race. Her practice times (in minutes and seconds) are 22:45, 21:56, 21:03, 20:33, and 20:28.

Find her mean time to complete the race.

Step 1 Change Jocelyn's practice times to seconds.
Step 2 Find the sum of the practice times. Divide by the number of times.
Step 3 Convert your answer to minutes and seconds.

Answer Key

1) 16

1/8 in

2) 3.6oC

3) The numbers 5 and 8 both appear three times, so there are two modes in the data set.

4)
a. mean
b. mode
c. range

5) 21:21

What is the difference between the highest and lowest numbers in the range?

The range is the difference between the highest and lowest value in a set of values. To find the range, put all the values in a series in descending order (highest to lowest) and subtract the lowest value from the highest. That will give you the difference which we call the range!