1.

Evaluate lower quartile and upper quartile from the following series.Variable510152025303540Frequency161822212414119

Answer»
VariableFrequency(f)Cumulative Frequency(c .f.)
51616
101834
152256
202177
2524101
3014115
3511126
409135
N = 135

Q1 = size of \((\frac{N+1}4)^{th}\) item

Or, Q= size of \((\frac{135+1}{4})^{th}\) item

= Q= 34th item

Upper Quartile

Q= size of 3 \((\frac{N+1}{4})^{th}\) item

or, Q1 = size of 3 \((\frac{135+1}{4})^{th}\) item

= Q1 = 102nd item

This corresponds to 115 in the cumulative frequency. Hence, upper quartile is 30.



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