Measures of Data Spread: Definition, Range, Deviation, Overlay, Quartiles and Formulas
Measures of Data Spread: Definition, Range, Deviation, Overlay, Quartiles and Their Formulas – How to measure the spread of data? On this occasion About the knowledge.co.id will discuss the formula for the size of the distribution of data and other things about it. Let's look at the discussion together in the article below to better understand it.
Measures of Data Spread: Definition, Range, Deviation, Overlay, Quartiles and Formulas
The size of the data spread is a measure that shows how far a data is spread from the average. Measures of the spread of data in statistical materials include ranges, overlays, and quartiles.
What is meant by range, stretch, and quartiles, here's the explanation:
- The range or range is the difference between the large data values and the smallest data values.
- The Inter-Quartile Spread or Range (JAK) is the difference between the upper quartile (Q3) and the lower quartile (Q1).
- Quartiles are the division of a number of sorted data into equal numbers for each section. Each section is separated by a quartile value which includes the lower quartile (Q1), the middle quartile (Q2), and the upper quartile (Q1).
There are measures of the spread of the data that we will study in this article, namely the range, average deviation, variety and standard deviation.
Range or Range or Range
In single data, we can easily find the maximum and minimum values. then what about group data? The range is the difference between the largest data and the smallest data. Range is often denoted by R.
Data Reach
R = xmax – xmin
Information:
R = reach
Xmax = largest data
Xmin = smallest data
Example of Data Range Problems
Determine the range of data: 3,6,10,5,8,9,6,4,7,5,6,9,5,2,4,7,8.
Answer :
R = xmax – xmin
= 10-2 = 8
So, the range of the data is 8.
Interquartile range
The interquartile range is the difference between the third and first quartiles.
H = Q3 – Q1
Information :
H = interquartile range
Q3 = third quartile
Q1 = first quartile
Quartile deviation (semi interquartile range)
The quartile deviation is half of the difference between the third and first quartiles.
Sk = ½ Q3 – Q1
Information :
Sk = quartile deviation
Q3 = third quartile
Q1 = first quartile
Average Deviation
The average deviation is the average value of the difference between each data and the mean or calculated average. The mean deviation is often denoted by SR.
Single Data
Information :
SR = mean deviation
Xi = data i
X = calculated average
n = lots of data
Categorized Data (Group)
Information :
SR = mean deviation
Xi = data i
X = calculated average
fi = i-th data frequency
Variety or Variation
Variety or variation is a value that indicates the magnitude of the spread of data in the data group. Variety or variation is denoted by s2.
Variation for single data
Information :
s2 = variation
xi = data to –i
x = calculated mean
n = lots of data
Variations for grouped data
Information :
s2 = variation
xi = data to –i
x = calculated mean
fi = i-th data frequency
Baku Devi
The standard deviation, also known as the standard deviation, is the square root of the deviation divided by the amount of data. The standard deviation is often denoted by s.
Standard deviation for single data
Information :
S = standard deviation
xi = data to –i
x = calculated mean
n = lots of data
Standard deviation for classified data
Information :
s = standard deviation
xi = data to –i
x = calculated mean
fi = i-th data frequency
Overlay (H) Or Inter-Quartile Range (JAK)
We can easily find the overlay value of a data, namely:
JAK = Q3-Q1
Quartile
- Quartiles are fractiles that divide a sorted data set into four equal parts
- The types of quartiles are lower quartile or Q1, middle quartile or Q2 and upper quartile or Q3
- The quartile groups based on the type of data are single data quartiles and group data quartiles
Below is a review of quartile data which includes quartile deviation, quartile mean, three quartile mean, and triad statistics.
- The quartile deviation or often also known as the semi-interquartile range is a value that shows half the time of the overlay. Obtained by subtracting the lower quartile from the upper quartile and then dividing by 2 (two).
- The mean of the quartiles is the average of the upper and lower quartiles. The way to get the average of the quartiles is to add up the upper and lower quartiles and then divide by 2 (two).
- The three quartile mean is the average of the three quartile values consisting of the upper, middle and lower quartiles. The way to get the average of the quartiles is to add up the three quartiles and then divide by 2 (two).
- While statistics is data consisting of five values, namely the highest value xmax, lowest value xmin, upper quartile (Q1), middle quartile (Q2), and lower quartile (Q3).
Problems example
Determine the range of data: 3,6,10,5,8,9,6,4,7,5,6,9,5,2,4,7,8.
Answer :
R = xmax – xmin
= 10-2 = 8
So, the range of the data is 8.
Thus the review from About the knowledge.co.id about Data Spread Size, hopefully can add to your insight and knowledge. Thank you for visiting and don't forget to read other articles.
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