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Answer to Question #3023 in Statistics and Probability for jenny

Question #3023
The following table gives the distributions
of marks in a class of 65 students :

Marks No. of students
0 —4 10
4 — 8 12
8 —12 18
12 —16 10
16 —20 5
20 — 24 4
24 and above 6

Calculate mode and semi-inter quartile
range.(please include details)
Expert's answer
The most frequently value in the data on the interval 8-12 , so m=(8+12)/2=10
The lower quartile (Q1) is the median of the lower half of the data set.
L_0.25=0.25*66=16.5
So Q1=(6+6)/2=6

Q3 is 3/4*(n+1) - th value in the data set: 3/4*66=49.5
Q3=(14+14)/2=14 (49-th and 50-th numbers in the data lie on the interval [12-16])

Marks No. of students comulative frequency
0 --4 & 10 & 10
4 -- 8 12 & 22
8 --12 18 & 40
12 --16 10 & 50 lt;<<<------
16 --20 5 55
20 -- 24 & 4 59
24 and above 6 65

semi-inter quartile range IQR = (Q3-Q1) / 2 = (14-6) / 2& = 8

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