Question

the mean of the observation : a , a + 1 , 2a + 3 , 3a + 1 and a - 1 is 12

Find the value of a.​

Answer 1

Answer:

Step-by-step explanation:

ANSWER:-

We need to know that:-

$\sf{Mean = \dfrac{Sum \ of \ Observations}{Number \ of \ Observations}}$

Using this, we will be able to solve the questions.

• Here, a , a + 1 , 2a + 3 , 3a + 1 and a - 1 are the observations.
• 12 is the mean.
• And number of Observations is 5.
• We need the value of a

$\dfrac{a+a+1+2a+3+3a+1+a-1}{5}=12$

$\dfrac{8a+4}{5}=12$

$8a+4=60$

$8a=56$

$\boxed{\bf{a=7}}$

Things to Note:-

• We need to remember the empirical Formula.
• We must carry out the addition carefully.

Answer 2

Given:-

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• The mean of the observation : a , a + 1 , 2a + 3 , 3a + 1 and a - 1 is 12

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To Find:-

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• The value of a

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STEP BY STEP EXPLANATION:-

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Mean = 12

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Sum of the observation

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$\sf \implies a + (a + 1) + (2a + 3) + (3a + 1) + (a - 1) = 8a + 1$

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Number of observation = 5

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$\sf \therefore12 = \frac{8a + 4}{5} \\ \\ \\ \sf\implies8a + 4 = 60 \\ \\ \\ \sf\implies a = 7 \: \: \: \: \: \: \: \: \: \: \: \: \:$

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∴ Thus, The value of a is 7