1: The marks of 19 students are given below:
41, 21, 38, 27,31,45,23,26,29,30,28,25,35,
42,47,50,29,31,35.
Calculate all the quartiles for the above
data.
Answers
Answer:
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Step-by-step explanation:
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Answer:
The lower , middle and upper quartile of the given data are 27 , 31, 41 respectively
Step-by-step explanation:
- In context to the given question, we have to find the value of all the quartile values of the given data.
- given data:
41,21,38,27,31,45,23,26,29,30,28,25,35,42,47,50,29,31,35.
Firstly by arranging the given data is ascending order;
21,23,25,26,27,28,29,29,30,31,31,35,35,38,41,42,45,47,50
There are three quartile namely, upper quartile , middle or median quartile and lower quartile
- First or Lower Quartile (Q1) divides the distribution in such a way that one-fourth (25\%) of total items fall below it and three-fourth (75%) fall above it.
- Middle or (Q2) or Median: divides the distribution in such a way that half (50%) of total items fall below it and half (50\%) above it.
- Upper Quartile (Q3):Q divides the distribution in such a way that three fourth (75%) of total items fall below it and one- fourth (25%) fall above it.
Middle quartile = [N(t h)+1]/2
where n is the total no of terms
middle quartile = [19+1]/ 2
Middle quartile = 20/2 = 10th term= 31
Middle quartile = 31
Now by finding, lower quartile
Lower quartile = [N(t h)+1] (1/4)
where n is the total no of terms
Lower quartile = [19+1]/ 4
Lower quartile = 20/4 = 5th term= 27
Lower quartile = 27
Lastly by finding Upper quartile
Upper quartile = [N(t h)+1] (3/4)
where n is the total no of terms
Upper quartile =[19+1] (3/4)
Upper quartile =60/4 = 15th term = 41
Upper quartile =41
Therefore, The lower , middle and upper quartile of the given data are 27 , 31, 41 respectively.