What Does Range Mean In Maths?
Contents
What is the range in math examples?
Problems and Solutions – Q.1: If the data set has observations as: 4, 6, 7, 5, 3, 5, 4, 5, 2, 6, 2, 5, 1, 9, 6, 5, 8, 4, 6, 7. Then find:
- (a) The maximum value?
- (b) The minimum value?
- (c) Range of data set
- Solution: Let us arrange the given values from lowest to highest (increasing order).
- 1, 2, 2, 3, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 8, 9.
- Clearly from the above arrangement, we can conclude that;
- (a) The maximum value is 9.
- (b) The minimum value is 1
- (c) Range = 9 – 1 = 8
Q.2: What is the arithmetic mean of 4, 6, 7, 5, 3, 5, 4, 5, 2, 6, 2, 5, 1, 9, 6, 5, 8, 4, 6, 7?
- Solution: To find the arithmetic mean, we have to use the below formula:
- Arithmetic mean = (Sum of all observations)/(Total number of observations)
- Sum of all observation = 1 + 2 + 2 + 3 + 4 + 4 + 4 + 5 + 5 + 5 + 5 + 5 + 6 + 6 + 6 + 6 + 7 + 7
- + 8 + 9 = 100
- Total Number of Observation = 20
- Arithmetic mean = (100/20) = 5
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In statistics, the range of observations is the value that is obtained from the difference between the highest and lowest values. To find the range of a given set of observations, we need to arrange them in ascending order first. Later, evaluate the difference between maximum and minimum values to get the range.
The formula for finding the range is given by: Range (X) = Highest observation – Lowest observation Here, the highest observation is 90 and the lowest observation is 3, therefore the range is the difference between 90 and 3, i.e.90 – 3 = 87. Mean represents the average value of a set of data whereas the range denotes the spread of observations.
The mean is equal to the ratio of the sum of all observations and the total number of observations but the range is the difference between maximum and minimum values in the observation. : Range in Statistics (Range Examples)
What does range mean in math in reading?
The range is the difference between the largest and smallest data points in a set of numerical data. The midrange is the average of the largest and smallest data points.
What is a domain and range in math?
Domain and Range. The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.
How do you find the range of the data set?
How to find the range for a set of data – AP Statistics
- Six homes are for sale and have the following dollar values in thousands of dollars:
- 535
- 155
- 305
- 720
- 315
- 214
What is the range of the values of the six homes? Possible Answers: Correct answer: Explanation : The range is the simplest measurement of the difference between values in a data set. To find the range, one simply subtracts the lowest value from the greatest value, ignoring the others. Here, the lowest value is 155 and the greatest is 720. Alice recorded the outside temperature at noon each day for one week. These were the results.
- Monday: 78
- Tuesday: 85
- Wednesday: 82
- Thursday: 84
- Friday: 82
- Saturday: 79
- Sunday: 80
What is the range of temperatures? Possible Answers: Correct answer: Explanation : The range is the simplest measurement of the difference between values in a data set. To find the range, simply subtract the lowest value from the greatest value, ignoring the others. Find the range for the set. Possible Answers: Correct answer: Explanation :
- To find the range, subtract the minimum value from the maximum value
- minimum:
- maximum:
- So,
- maximum – minimum =
A business tracked the number of customer calls received over a period of five days. What was the range of customer calls received daily?
- Day 1: 57
- Day 2: 63
- Day 3: 48
- Day 4: 49
- Day 5: 59
Possible Answers: Correct answer: Explanation :
- The range is the simple measurement of the difference between values in a dataset.
- To find the range, simply subtract the lowest value from the greatest value, ignoring the others.
Find the range for the set of data Possible Answers: Correct answer: Explanation :
- The range is equal to the absolute difference between the minimum and maximum value.
- We find the range to be
- Let be a positive integer.
- What is the range of the set.
Possible Answers: Correct answer: Explanation :
- To find the range, subtract the minimum value from the maximum value
- minimum:
- maximum:
- So,
- maximum – minimum =
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What is range in distance?
Range or distance measurement Figure 1: Runtime measurement by radar 
transmitted energieecho signalFigure 1: Runtime measurement by radar
Figure 1: Runtime measurement by radar The radar transmits a short radio pulse with very high pulse power. This pulse is focused in one direction only by the directivity of the antenna, and propagates in this given direction with the speed of light. If in this direction is an obstacle, for example an airplane, then a part of the energy of the pulse is scattered in all directions.
- A very small portion is also reflected back to the radar.
- The radar antenna receives this energy and the radar evaluates the contained information.
- The distance we can measure with a simple oscilloscope.
- On the oscilloscope moves synchronously with the transmitted pulse a luminous point and leaves a trail.
The deflection starts with the transmitter pulse. The luminescent spot moves to scale on the oscilloscope with the radio wave. At this moment, in which the antenna receives the echo pulse, this pulse is also shown on the oscilloscope. The distance between the two shown pulses on the oscilloscope is a measure of the distance of the aircraft.
- Since the propagation of radio waves happens at constant speed (the speed of light c 0 ) this distance is determined from the runtime of the high-frequency transmitted signal.
- The actual range of a target from the radar is known as,
- Slant range is the line of sight distance between the radar and the object illuminated.
While ground range is the horizontal distance between the emitter and its target and its calculation requires knowledge of the target’s elevation. Since the waves travel to a target and back, the round trip time is dividing by two in order to obtain the time the wave took to reach the target. 
(1)
c 0 = speed of light = 3·10 8 m / s t = measured runtime R = slant range antenna – aim
The distances are expressed in kilometers or nautical miles ( 1 NM = 1.852 km ). Range is the distance from the radar site to the target measured along the line of sight. (2) (3) The factor of two in the equation comes from the observation that the radar pulse must travel to the target and back before detection, or twice the range. (4) Where c 0 = 3·10 8 m / s, is the speed of light at which all electromagnetic waves propagate. If the respective running time t is known, then the distance R between a target and the radar set can be calculated by using this equation.
How do I calculate domain and range?
Domain and Range Calculator, Practice Problems, and Answers – Add New Question
- Question What is the domain and range of the function: f(x)=3x-12x+5? If you simplify the function, you can see that it’s f(x) = -9x + 5, which is a linear function. Linear functions go infinitely in every direction, and therefore both the domain and the range of the function are negative to positive infinity.
- Question How do I find the range of a function without graphing? Looking at a list of ordered pairs (a relation and possibly a function), the y-values (second values) in each ordered pair make up the range. You should list them in order from least to greatest. No graphing is required.
- Question How to find the domain of 1/√x+|x|? You need x to be non-negative in order to be able to compute its square root. X also cannot be zero, or else you will be dividing by zero. Any strictly positive value of x is fine to be in the domain, because both the square root and the division steps are allowed. In interval notation, say the domain of x is (0, infinity).
See more answers Ask a Question 200 characters left Include your email address to get a message when this question is answered. Submit Advertisement Article Summary X The domain of a function is the collection of independent variables of x, and the range is the collection of dependent variables of y.
- To find the domain of a function, just plug the x-values into the quadratic formula to get the y-output.
- To find the range of a function, first find the x-value and y-value of the vertex using the formula x = -b/2a.
- Then, plug that answer into the function to find the range.
- To properly notate the range, write out the numbers in brackets if they’re included in the domain or in parenthesis if they’re not included in the domain.
To learn how to find the range of a function graphically, read on! Did this summary help you? Thanks to all authors for creating a page that has been read 264,135 times.
What is domain and range examples?
Domain and Range The domain of a f ( x ) is the set of all values for which the function is defined, and the range of the function is the set of all values that f takes. (In grammar school, you probably called the domain the replacement set and the range the solution set. They may also have been called the input and output of the function.) Example 1: Consider the function shown in the diagram. Here, the domain is the set, D is not in the domain, since the function is not defined for D, The range is the set,2 is not in the range, since there is no letter in the domain that gets mapped to 2, You can also talk about the domain of a, where one element in the domain may get mapped to more than one element in the range.
- Example 2: Consider the relation,
- Here, the relation is given as a set of ordered pairs.
- The domain is the set of x -coordinates,, and the range is the set of y -coordinates,,
- Note that the domain elements 1 and 2 are associated with more than one range elements, so this is not a function.
- But, more commonly, and especially when dealing with graphs on the coordinate plane, we are concerned with functions, where each element of the domain is associated with one element of the range.
(See The,)
- Example 3:
- The domain of the function
- f ( x ) = 1 x
is all real numbers except zero (since at x = 0, the function is undefined: division by zero is not allowed!). The range is also all real numbers except zero. You can see that there is some point on the curve for every y -value except y = 0, Domains can also be explicitly specified, if there are values for which the function could be defined, but which we don’t want to consider for some reason.
- Example 4:
- The following notation shows that the domain of the function is restricted to the interval ( − 1, 1 ),
- f ( x ) = x 2, − 1 < x < 1
The graph of this function is as shown. Note the open circles, which show that the function is not defined at x = − 1 and x = 1, The y -values range from 0 up to 1 (including 0, but not including 1 ). So the range of the function is 0 ≤ y < 1, : Domain and Range
What is the difference between domain and range in math a level?
Functions – Algebra – Mathematics A-Level Revision This section looks at functions within the wider topic of Algebra. A function may be thought of as a rule which takes each member x of a set and assigns, or maps it to the same value y known at its image.
- Example
- f (4) = 4 2 + 5 =21, f (-10) = (-10) 2 +5 = 105 or alternatively f : x → x 2 + 5,
- The phrase “y is a function of x” means that the value of y depends upon the value of x, so:
- y can be written in terms of x (e.g. y = 3x ).
- If f(x) = 3x, and y is a function of x (i.e. y = f(x) ), then the value of y when x is 4 is f(4), which is found by replacing x”s by 4″s,
- Example
- If f(x) = 3x + 4, find f(5) and f(x + 1).
- f(5) = 3(5) + 4 = 19 f(x + 1) = 3(x + 1) + 4 = 3x + 7
- Domain and Range
The domain of a function is the set of values which you are allowed to put into the function (so all of the values that x can take). The range of the function is the set of all values that the function can take, in other words all of the possible values of y when y = f(x).
So if y = x 2, we can choose the domain to be all of the real numbers. The range is all of the real numbers greater than (or equal to) zero, since if y = x 2, y cannot be negative. One-to-One We say that a function is one-to-one if, for every point y in the range of the function, there is only one value of x such that y = f(x).
f(x) = x 2 is not one to one because, for example, there are two values of x such that f(x) = 4 (namely –2 and 2). On a graph, a function is one to one if any horizontal line cuts the graph only once.
- Composing Functions
- fg means carry out function g, then function f. Sometimes, fg is written as fog
- Example
- If f(x) = x 2 and g(x) = x – 1 then gf(x) = g(x 2 ) = x 2 – 1 fg(x) = f(x – 1) = (x – 1) 2
- As you can see, fg does not necessarily equal gf
- The Inverse of a Function
The inverse of a function is the function which reverses the effect of the original function. For example the inverse of y = 2x is y = ½ x, To find the inverse of a function, swap the x”s and y”s and make y the subject of the formula.
- Example
- Find the inverse of f(x) = 2x + 1 Let y = f(x), therefore y = 2x + 1 swap the x”s and y”s: x = 2y + 1 Make y the subject of the formula: 2y = x – 1, so y = ½(x – 1)
- Therefore f -1 (x) = ½(x – 1)
- f -1 (x) is the standard notation for the inverse of f(x). The inverse is said to exist if and only there is a function f -1 with ff -1 (x) = f -1 f(x) = x
- Note that the graph of f -1 will be the reflection of f in the line y = x.
- Graphs
Functions can be graphed. A function is continuous if its graph has no breaks in it. An example of a discontinuous graph is y = 1/x, since the graph cannot be drawn without taking your pencil off the paper: A function is periodic if its graph repeats itself at regular intervals, this interval being known as the period. A function is even if it is unchanged when x is replaced by -x, The graph of such a function will be symmetrical in the y-axis. Even functions which are polynomials have even degrees (e.g.
- Y = x²). A function is odd if the sign of the function is changed when x is replaced by -x,
- The graph of the function will have rotational symmetry about the origin (e.g. y = x³).
- The Modulus Function The modulus of a number is the magnitude of that number.
- For example, the modulus of -1 ( |-1| ) is 1.
- The modulus of x, |x|, is x for values of x which are positive and -x for values of x which are negative.
So the graph of y = |x| is y = x for all positive values of x and y = -x for all negative values of x: Transforming Graphs If y = f(x), the graph of y = f(x) + c (where c is a constant) will be the graph of y = f(x) shifted c units upwards (in the direction of the y-axis). If y = f(x), the graph of y = f(x + c) will be the graph of y = f(x) shifted c units to the left. If y = f(x), the graph of y = f(x – c) will be the graph of y = f(x) shifted c units to the right.
- If y = f(x), the graph of y = af(x) is a stretch of the graph of y = f(x), scale factor (1/a), parallel to the x-axis.
- Example
- The graph of y = |x – 1| would be the same as the above graph, but shifted one unit to the right (so the point of the V will hit the x-axis at 1 rather than 0).
: Functions – Algebra – Mathematics A-Level Revision
What is domain and range examples?
Domain and Range The domain of a f ( x ) is the set of all values for which the function is defined, and the range of the function is the set of all values that f takes. (In grammar school, you probably called the domain the replacement set and the range the solution set. They may also have been called the input and output of the function.) Example 1: Consider the function shown in the diagram. Here, the domain is the set, D is not in the domain, since the function is not defined for D, The range is the set,2 is not in the range, since there is no letter in the domain that gets mapped to 2, You can also talk about the domain of a, where one element in the domain may get mapped to more than one element in the range.
Example 2: Consider the relation, Here, the relation is given as a set of ordered pairs. The domain is the set of x -coordinates,, and the range is the set of y -coordinates,, Note that the domain elements 1 and 2 are associated with more than one range elements, so this is not a function. But, more commonly, and especially when dealing with graphs on the coordinate plane, we are concerned with functions, where each element of the domain is associated with one element of the range.
(See The,)
- Example 3:
- The domain of the function
- f ( x ) = 1 x
is all real numbers except zero (since at x = 0, the function is undefined: division by zero is not allowed!). The range is also all real numbers except zero. You can see that there is some point on the curve for every y -value except y = 0, Domains can also be explicitly specified, if there are values for which the function could be defined, but which we don’t want to consider for some reason.
- Example 4:
- The following notation shows that the domain of the function is restricted to the interval ( − 1, 1 ),
- f ( x ) = x 2, − 1 < x < 1
The graph of this function is as shown. Note the open circles, which show that the function is not defined at x = − 1 and x = 1, The y -values range from 0 up to 1 (including 0, but not including 1 ). So the range of the function is 0 ≤ y < 1, : Domain and Range
