Find the 3 quartiles in the following data set: 4 5 8 7 11 9 9.
Solution:
A quartile divides data into three points:
- Lower quartile(Q₁)
- Median(Q₂)
- Upper Quartile(Q₃)
To find the 3 quartiles, arrange the data points in ascending order. 4 5 7 8 9 9 11.
Here n = number of data points given = 7
Lower Quartile formula is the (n+1)/4th term
= (7 + 1)/4 = 2nd term of the series
The second term of the given series is 5. Hence the lower quartile is 5.
The next quartile is actually the median and that is the (n+1)/2th term or Q₁
The middle quartile or the median (Q₂) = (7 + 1)/2 = 4th term
The fourth term of the series is 8. Hence the middle quartile is 8.
The Upper quartile is the 3(n+1)/4th term or Q₃
The 3(n+1)/4th term = 3(7 + 1)/4 = 6 th term of the series.
The sixth term of the series is 9. Hence the upper quartile is 9.
Thus the three quartiles Q₁, Q₂ and Q₃ are 5, 8 and 9 respectively.
Find the 3 quartiles in the following data set: 4 5 8 7 11 9 9.
Summary:
The three quartiles are basically positional identities of a given series of numbers. The three quartiles of the given number series i.e. 4 5 8 7 11 9 9 are Q₁ = 5; Q₂ = 8 and Q₃ = 9.
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