Question

can you please help me with this question ​

Answer 1

Step-by-step explanation:

Given:

x__10__20__30__40__50__60

f__4____k___8___p___3___4

To find: Value of k and p,if mean is 34.

Solution:

Step 1: Find equation of k and p with given frequency

$4 + k + 8 + p + 3 + 4 = 35 \\ \\ k + p = 35 - 19 \\ \\ \bold{\red{k + p = 16}}...eq1$

Step 2: Find equation of k and p,with given mean

We know that

$\boxed{\bold{\overline{x}=\dfrac{\Sigma x_if_i}{f}}}$

Thus,

$34 = \frac{10 \times4 + 20 \times k + 30 \times 8 + 40 \times p + 50 \times 3 + 60 \times 4 }{35} \\ \\ 1190 = 40 + 20k + 240 + 40p + 150 + 240 \\ \\ 1190 = 20k + 40p + 670 \\ \\ 20k + 40p = 1190 - 670 \\ \\ 20k + 40p = 520 \\ \\ or \\ \\ \bold{\green{k + 2p = 26}}...eq2$

Step 3: Solve eq1 and eq2

Subtract both equations

$k + p = 16 \\ k + 2p = 26 \\ ( - ) \: \: ( - ) \: \: ( - ) \\ - - - - - - \\ - p = - 10 \\ \\ \bold{p = 10 }$

put the value of p in eq1

$k + 10 = 16 \\ \\\bold{ k = 6 }$

Final answer:

Value of k=6 and p=10.

Hope it helps you.

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