Range in Math
- What Do You Mean by Range in Math?
- How to Find the Range of a List of Numbers
- Some Examples of Range in Math
- The Range Between Two Numbers
- Comparison of Data Using a Range
- How to Find Range from Graph
- Solved Examples
- Practice Problems
- Frequently Asked Questions
What Do You Mean by Range in Math?
The range of a collection of numbers is the distance between the largest and smallest numbers in the collection. We subtract the smallest value from the biggest value to determine a set of numbers' range.
Mathematicians use the range to interpret a sample of numbers. It can be used to check how far is the lowest from the highest value in a list of numbers.
For example, for the given list of numbers `{2, 5, 1, 7, 10}` the range is `10 - 1 = 9`.
How to Find the Range of a List of Numbers
The range of a given list of numbers is equal to the difference between the largest and smallest number.
Range `=` Largest number `-` Smallest Number
Some Examples of Range in Math
Example `1`: What is the range of numbers `{55, 21, 90, 65, 17}`?
Solution:
The largest number `= 90`
The smallest number `= 17`
So, the range `= 90 - 17 = 73`
Example `2`: The given data shows the scores (out of `100`) of `6` students in the maths quiz. What is the range of the scores?
Solution:
The highest score `= 92`
The lowest score `= 35`
So, the range of scores `= 92 - 35 = 57`
The Range Between Two Numbers
The range is the difference between the two numbers for a list of numbers having only two numbers.
The range of a list having two numbers `{18, 29}` is `29 - 18 = 11`.
Comparison of Data Using a Range
Let’s understand how we can compare data using a range in math.
Example `1`: Price for a microwave oven (in dollars) in different years for two different shops are as follows:
Solution:
Range of prices for Shop `A = 132 - 100 = 32`
Range of prices for Shop `B = 135 - 88 = 47`
So, it can be said that there is more variability in the price of microwave ovens for Shop `B` as compared to Shop `A`.
How to Find Range from Graph
Data can be represented in different forms like bar graphs, scatter plots, etc. We can find range from graphs as well.
Example `1`: A bar graph below shows the number of goals scored by Year `10` Football Team across the last `15` matches they played. Find the range of goals scored.
Solution:
Highest value `=` Highest number of goals scored in a match `= 4`
Lowest value `=` Lowest number of goals scored in a match `= 0`
Range of goals scored by the team over the last `15` matches `= 4 - 0 = 4`
Solved Examples
Example `1`: Given below are the costs of a lollipop of a certain brand in ten different countries. Find the range.
Solution:
Highest cost of the lollipop `= $ 2.20`
Lowest cost of the lollipop `= $ 0.70`
So, the range of the cost of the lollipop is `$2.20 - $0.70 = $1.50`.
Example `2`: Find the range of the first five even numbers.
Solution:
The first five even numbers are: `2, 4, 6, 8,` and `10`.
Highest value `= 10`
Lowest value `= 2`
So, the range of the first five even numbers is `10 - 2 = 8`.
Example `3`: Find the range of the list of numbers given below:
`{9, 5, 15, 10, 22, 2}`
Solution:
Highest value `= 22`
Lowest value `= 2`
So, the range is `22 - 2 = 20`.
Practice Problems
Q`1`. Scores of a player in five matches are `{ 6, 19, 35, 30, 12 }`. Find the range of the player’s score.
- `35`
- `19`
- `30`
- `29`
Answer: d
Q`2`. Find the range of data given below:
- `425`
- `402`
- `425`
- `378`
Answer: a
Q`3`. The range of a dataset is `25`, and the minimum value is `15`. What is the maximum value?
- `40`
- `30`
- `50`
- `65`
Answer: a
Q`4`. The range of a dataset is `15`, and the maximum value is `42`. What is the minimum value?
- `37`
- `30 `
- `18 `
- `27 `
Answer: d
Frequently Asked Questions
Q`1`. What is the range of a data set?
Answer: The range of a data set is the difference between the maximum and minimum values in the set. It provides a measure of the spread or dispersion of the data.
Q`2`. How is the range affected by outliers in a data set?
Answer: If there are unusual or very high/low numbers in our data, called outliers, they can make the range seem larger. Outliers can stretch the range because they are way off from the average or middle values, pulling the highest and lowest numbers farther away from where most of the data is.
Q`3`. Can the range be negative?
Answer: No, the range is always a non-negative value. It is calculated as the absolute difference between the maximum and minimum values, ensuring a positive result.
Q`4`. How can you find the range if the data set is not given explicitly?
Answer: If the data set is not explicitly provided but includes extreme values, you can find the range by subtracting the minimum from the maximum value.