Q9) Find inter quartile range, Quartile Deviation and coefficient of quartile deviation from the following data: Х 0-5 10-15 20-25 25-30 5-10 10 15-20 12 F 6 20 6 6
Answers
Explanation:
XMid point (x) Frequency (F) i=class interval width A=22.5 Assumed mean u=ix−A fu0-5 2.5 3 5 22.5 -4 -12 5-10 7.5 5 5 22.5 -3 -15 10 -1512.5 7 5 22.5 -2 -14 15-20 17.5 8 5 22.5 -1 -8 20-25 22.5=A 10 5 22.5 0 0 25-30 27.5 11 5 22.5 1 11 30-35 32.5 14 5 22.5 2 28 35-40 37.5 19 5 22.
5 3 57 40-45 42.5 15 5 22.5 4 60 45-50 47.5 13 5 22.5 5 65 Σf=105 Σfu=172
The formula used for arithmetic mean of grouped data by step deviation method is, X=A+∑f∑fu×i
A= Assumed mean of the given data
∑ = Summation of the frequencies given in the grouped data
∑fu = Summation of the frequencies and deviation of a given mean data
u=i(x−A)
i= Class interval width
X = arithmetic mean
X=22.5+105172×5
=22.5+8.19
=30.69 ≈ 31
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SIMILAR QUESTIONS
Find the arithmetic mean using step deviation method for the following. The data shows distance covered by 40passengers to perform their work. (Round off your answer to the nearest whole number).
Distance (km)
1-5
5-9
9-13
13-17
17-21
21-25
25-29
Number of passengers
2
4
6
8
10
Answer:
The Quartile Deviation is a simple way to estimate the spread of a distribution about a measure of its central tendency (usually the mean). So, it gives you an idea about the range within which the central 50% of your sample data lies. Consequently, based on the quartile deviation, the Coefficient of Quartile Deviation can be defined, which makes it easy to compare the spread of two or more different distributions. Since both of these topics are based on the concept of quartiles, we’ll first understand how to calculate the quartiles of a dataset before working with the direct formulae.