How Many Values Are In The Range 17 To 118

In Statistics, yous might have studied the methods of finding a representative value for the given data, i.east. the mensurate of central tendency. To remember, mean, median, and fashion are 3 measures of fundamental tendency. As we know, measuring key tendency gives us an thought of where information points are centred. Even so, to interpret the data thoroughly, nosotros should also run across how the data are scattered. And how much they have bunched most a measure of central trend.

Range in Statistics

Every bit the measures of central tendency are non enough to requite complete information well-nigh a given information. Variability is another determinant that is required to be studied nether statistics. Like to measures of primal trend, we demand to accept a single number to describe variability. This single number has expressed a mensurate of dispersion. In this article, you lot will larn about one of the measures of dispersion called range.

Range Pregnant

In statistics, the difference between the highest and lowest observations in a given data is called its Range.

Range Formula

The formula to calculate the range of a data fix is given beneath:

Range = Maximum value – Minimum value

However, we can ascertain the formulas to find the range of grouped and ungrouped data.

Range of Ungrouped Data

The formula to find the range of ungrouped data or detached distribution of data is given every bit:

Range = Highest value of the data gear up – Lowest value of the data set

Range of Grouped Data

In the case of continuous frequency distribution or grouped data, the range is defined equally the difference between the upper limit of the maximum interval of the grouped data and the lower limit of the minimum interval. It is the simplest measure of dispersion. It gives a comprehensive view of the total spread of the observations. Thus, the formula to calculate the range of a grouped information is given below:

Range = Upper-class purlieus of the highest interval – Lower class boundary of the lowest interval

How to Detect the Range

To empathise the method of calculating range for different types of information in statistics, go through the solved examples given beneath. These examples assist in understanding how to find the range for detached and continuous data.

Solved Examples

Example 1: Observe the range of the data: 21, 6, 17, 18, 12, 8, 4, xiii

Solution:

Given,

21, 6, 17, 18, 12, 8, 4, xiii

Highest value = 21

Everyman value = 4

Range = Highest value – Everyman value

= 21 – 4

= 17

Example 2: Age (in years) of half-dozen boys and 6 girls are recorded every bit below:

Girls	6	7	nine	8	x	10
Boys	7	nine	12	14	13	17

(a) Notice the range for each group.

(b) Find the range if the two groups are combined together.

Solution:

(a) The range for group of girls = x – half dozen = 4

The range for group of boys = 17 – 7 = 10

(b) If the ages of the group of boys and girls are combined, then the range will be:

17 – four = 13

Example iii: Calculate the range for the given frequency distribution.

Grade Interval	10 – twenty	20 – 30	30 – 40	40 – l	50 – 60	60 – seventy	70 – 80
Frequency	2	3	14	8	three	8	2

Solution:

We know that the range of grouped data is given by the formula:

Range = Upper-class boundary of the highest interval – Lower class boundary of the lowest interval

Here, the Upper-class boundary of the highest interval = 80

Lower class boundary of the everyman interval = ten

Therefore, range = 80 – ten = 70

Example 4: Find the range of the post-obit data.

CI	16 – xx	21 – 25	26 – xxx	31 – 35	36 – xl	41 – 45	46 – 50	51 – 55
f	5	six	12	14	26	12	16	9

Solution:

Given data is not continuous frequency distribution.

Now, nosotros have to convert the given data into continuous frequency distribution past subtracting 0.5 from the lower limit and adding 0.5 to the upper limit of each form interval.

CI	15.5 – 20.5	xx.five – 25.5	25.v – xxx.5	30.v – 35.5	35.5 – forty.5	40.5 – 45.v	45.v – fifty.5	50.5 – 55.5
f	5	6	12	xiv	26	12	xvi	9

Here,

Upper-grade boundary of the highest interval = 55.v

Lower class boundary of the lowest interval = 15.5

Therefore, range = 55.5 – 15.5 = 40

Practice Problems

1. 1. The marks in a subject for 12 students are as follows:

      31, 37, 35, 38, 42, 23, 17, 18, 35, 25, 35, 29

      For the given data, discover the range.

   2. Given below are heights of 15 students of a form measured in cm:

128, 144, 146, 143, 136, 142, 138, 129, 140, 152, 144, 140, 150, 142, 154

Find the range of the given data.

1. Calculate the range of the information given below:

Class	thirty – 40	40 – 50	50 – 60	60 – lxx	70 – 80	eighty – 90	ninety – 100
Frequency	ii	iii	viii	15	12	seven	3

For more than concepts related to range and measures of dispersion, download BYJU'S – The Learning App today!

Frequently Asked Questions on Range

What does Range mean in statistics?

In statistics, the range is the deviation betwixt maximum and minimum values of a data set.

How exercise you detect the range?

We tin find the range of dissimilar types of information using the specified formulas.
For ungrouped information, range = Highest value of the data fix – Everyman value of the data set
For grouped data, range = Upper-course boundary of the highest interval – Lower class boundary of the lowest interval

Is Range e'er positive?

Yes, the value of a range of whatsoever given data set up is either zero or a positive number.

What is the range of a listing of numbers?

The range of a listing of numbers is the deviation betwixt the largest and smallest values of that list of numbers.

Can the range be negative?

No, since the range is equal to the difference between highest and everyman numbers, it is e'er zero or a positive number.

Source: https://byjus.com/maths/range/

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