The following is the distribution of 160 workers according to the wages in a certain factory wages more no. of workers than 8000 160 9000 155 1 137 11000 97 12000 57 13000 23 14000 10 15000 1 16000 0 determine the values of all quartiles and interpret the results
Answers
Step-by-step explanation:
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Given :
Wages No. of workers
more than 8000 160
more than 9000 155
more than 10000 137
more than 11000 97
more than 12000 57
more than 13000 23
more than 14000 10
more than 15000 1
more than 16000 0
To find :
Q₁ , Q₂ , Q₃ and interpret the result
Solution :
CI f cf
8000 - 9000 5 5
9000 - 10000 18 23
10000 - 11000 40 63 Q₁ class
11000 - 12000 40 103 Q₂ class
12000 - 13000 34 137 Q₃ class
13000 - 14000 13 150
14000 - 15000 9 159
15000 - 16000 1 160
q₁ = N / 4 = 160 / 4 = 40
Q₁ = L₁ + (q₁ - c) * (L₂ - L₁)
f
Q₁ = 10000 + (40 - 23) * (11000 - 10000)
40
Q₁ = 10425
q₂ = 2N / 4 = N / 2 = 2 * 160 / 4 = 80
Q₂ = L₁ + (q₂ - c) * (L₂ - L₁)
f
Q₂ = 11000 + (80 - 63) * (12000 - 11000)
40
Q₂ = 11425
q₃ = 3N / 4 = 3 * 160 / 4 = 120
Q₃ = L₁ + (q₃ - c) * (L₂ - L₁)
f
Q₃ = 12000 + (120 - 103) * (13000 - 12000)
34
Q₃ = 12500
Therefore,
Q₁ = 10425
Q₂ = 11425
Q₃ = 12500
And from the result we can say that Q₁<Q₂<Q₃.