Quartile Deviation Formula: Definition, Types and Example Problems
Quartile Deviation Formula: Definition, Types and Example Problems – What is the quartile deviation and what is the formula for it?, On this occasion About the knowledge.co.id will discuss it and of course other things that also cover it. Let's look at the discussion together in the article below to better understand it.
Quartile Deviation Formula: Definition, Types and Example Problems
Quartiles are measures that divide data into four equal parts. As explained above, the quartiles consist of the lower quartile (Q₁), the middle quartile (Q₂/median) and the upper quartile (Q₃).
The quartile deviation is half of the difference between the upper and lower quartiles.
Quartile deviation = ½ (Q₃ – Q₁)
Quartiles are obtained by:
- Sort data from smallest to largest value
- Determine the median or
- Determine
(the median data is less than
) And
(the median data is more than
Quartile Deviation
Quartile Deviation or so-called Semi Interquartile Range is Half of the quartile range.
K3 – K1. or with JAK = range between quartiles, K3 = 3rd quartile, K1 =1st quartile).
Standard Value (z-Score)
Suppose we have a sample of size n (amount of data = n), and from the data x1, x2, x3,…,xn. Then the average = x.
And the standard deviation = s. Formed new data: z1, z2, z3,…, zn by using Coefficient of Variation.
Coefficient of Variation
KV =JAK = K3 – K1
Semi Inter-Quartile Range = 1/2 (K3 – K1)
Quartile Notation: q
Types of Quartile Deviation
Below are 3 types of quartiles, including:
- Lower Quartile (Q1)
The first step is to find the lower quartile value, then Bb (lower limit of the quartile value) is obtained, fk (cumulative frequency) is obtained from the number of frequencies just above the frequency data. Then fQ1 is the frequency of the data itself.
- Middle Quartile (Q2)
By first finding the middle quartile value, then obtaining Bb (lower limit of the quartile value), fk (cumulative frequency) is obtained from the number of frequencies just above the frequency data. Then fme is the frequency of the data itself.
- Upper Quartile (Q3)
By first looking for the upper quartile value, then obtaining Bb (lower limit of the quartile value), fk (cumulative frequency) is obtained from the number of frequencies just above the frequency data. Then fQ3 is the frequency of the data itself.
Quartiles divide consecutive data (n) into 4 equal parts.
——|——|——-|——-
Q1 Q2 Q3
Q1 = lower quartile (1/4n )
Q2 = middle quartile/median (1/2n)
Q3 = upper quartile (1/4n )
If we want to determine quartile values, the data must be sorted first from smallest to largest.
If the number of data n is odd
Q₁ = data to ¼ (n + 1)
Q₂ = data to ½ (n + 1)
Q₃ = data to ¾ (n + 1)
If the number of data n is even
Q₁ = data to ¼ (n + 2)
Q₂ = ½ (data to ½ n + data to (½ n + 1))
Q₃ = data to ¼ (3n + 2)
Discussion
In determining the quartile deviation, you have to find the 1st and 3rd quartiles first, then all we have to do is enter them into the formula, namely:
Quartile deviation = ½ (Q₃ – Q₁)
Example
Determine the quartile deviation if Q1 = 40.27 And Q3 = 53.79 !!!
Answer :
Qd = (1/2)(Q3 – Q1)
Qd = (1/2)(53.79 – 40.27)
Qd = (1/2)(13,52)
Qd = 6.76
So the quartile deviation is 6,76
Problems example
Given data 95, 84, 86, 90, 93, 88, 97, 98, 89, 94
Data is sorted first, becomes:
84 86 818 89 90 93 94 915 97 98
Q1 = 88; Q2 = 90 93; Q3s = 95
- Range J = 98 – 84 = 14
b. Q1=88 quartile; Q2 = (90+93)/2 = 91.5; Q3s = 95
Quartile deviation = Qd = (95 – 88) / 2 = 3.5
c. Average
= (88+86+88+89+90+93+95+97+98)/10 = 91,4
Standard deviation = Ö(((84-91.4)² + …… + (98-91.4)²)/10) = 4.72 - Data is grouped
| Score | Midpoint | Frequency |
| 50-54 | 52 | 4 |
| 55-59 | 57 | 6 |
| 60-64 | 62 | 8 |
| 65-69 | 67 | 16 |
| 70-74 | 72 | 10 |
| 75-79 | 77 | 3 |
| 80-84 | 82 | 2 |
| 85-89 | 87 | 1 |
| n = 50 |
- Range = Highest class midpoint – Lowest class midpoint = 87-52 =35
- Lower quartile (¼n )
Q1 = 59.5 + ((12.5 – 10)/8. (5)) = 61,06
Lower quartile (¾n )
Q3 = 69.5 + (37.5 – 34)/10. 5 = 71,25
Quartile Deviation
Qd = (Q3 – Q1) / 2 = (71.25 – 61.06) / 2 = 5.09
Semi interquartile range = quartile deviation = Qd = ½H = ½(Q3-Q1)
- Average
x = ((4)(52) + (6)(57) + … + (1)(870) / 50 = 66.4 - Baku Devi
___________________________________
Ö((52-66,4)² + …… + (87-66,4)²)/50 = 7,58
Semi interquartile range = quartile deviation = Qd = ½H = ½(Q3-Q1)
NOTES:
- If in a data set, each data is added / subtracted by a number, then:
– changing statistical values: Mean, Median, Mode, Quartiles.
– fixed statistical values: Range, Quartile Deviation, Standard deviation. - If in a data set, each data is multiplied by a number, then: all statistical values change.
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