Dynamics and StatisticsMedium

Question

If the mean of the data

Class $$5 - 10$$ $$10 - 15$$ $$15 - 20$$ $$20 - 25$$ $$25 - 30$$ $$30 - 35$$
Frequency 2 k 28 54 $$k + 1$$ 5

is 21 , then k is one of the roots of the equation :

Options

A.$2x^{2} - 23x - 10 = 0$
B.$4x^{2} - 35x + 24 = 0$
C.$2x^{2} - 19x - 10 = 0$
D.$2x^{2} - 35x + 98 = 0$

Solution

Sol. [Key Concept: Set $\Sigma\ fx/\Sigma\ f = 21$, solve for $k$, then choose the quadratic having $k$ as a root.]

Class $$5 - 10$$ $$10 - 15$$ $$15 - 20$$ $$20 - 25$$ $$25 - 30$$ $$30 - 35$$
Freq. 2 k 28 54 $$k + 1$$ 5

mean

$${21 = \frac{15 + 12.5k + 490 + 1215 + 27.5 + 27.5k + 162.5}{90 + 2k} }{1890 + 42k = 1910 + 40k }{k = 10 }$$

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