Math, asked by abinandmidhun4133, 1 year ago

Find the range and the quartile deviation for the following distribution.
\begin{tabular}{|l|c|c|c|c|c|c|c|}C.I. & 0-15 & 15-30 & 30-45 & 45-60 & 60-75 & 75-90 & 90-105 \\f_{i}  & 8 & 26 & 30 & 45 & 20 & 17 & 4\end{tabular}

Answers

Answered by imhkp4u
0

Answer:

Quartile Deviation = 21.78 [Ans]

Step-by-step explanation:

Class Interval   Frequency    Cumulative Frequency

    0 - 15                    8                            8

    15 - 30                 26                          34

   30 - 45                 30                           64

   45 - 60                 45                          109

   60 - 75                 20                          129

   75 - 90                  17                           146

   90 - 105                 4                            150

Position of Quartile 1 = 150/4 = 37.5th i.e. 30 - 45 range

Position of Quartile 3 = 150 * (3/4) = 112.5th i.e. 60 - 75 range

Q1 = 30 + 15 * \frac{\frac{(150-34)}{4} }{30} = 15 * \frac{29}{30} = 44.5

Q3 = 60 + 15 * \frac{\frac{3}{4}*(150-109) }{20} = 83.0625

Quartile Deviation = (Q3 - Q1) / 2 = (83.0625 - 44.5)/2 = 21.78 [Ans]


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