Question

If the average of x, 2x-8, 2x+2, 3x-1, and 4x + 1 is 6, what is the mode of these numbers?
3
13
2
8.​

Answer 1

Answer:

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Answer 2

★ How to do :-

Here, we are given with some of the observations in the form of variables and the average of all those observations. We aren't given with each of the observation in the numerical format. All of them are in the form of variables and some constants. We are asked to find the mode of the data. To find the mode of any data, we first should know the value of the observations in the given data. So, first we should find the value of each of the observation by the formula of average. We can substitute the value of average in it's place and the given variables on the numerators and the number of observations in the denominator. Then, we can find the value of x by the concept of transposition method. Then, we can find the value of each observations of the data. Finally, we can find the mode. So, let's solve!!

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➤ Solution :-

${\sf \leadsto \underline{\boxed{\sf Average = \dfrac{Sum \: of \: all \: observations}{Number \: of \: observations}}}}$

Substitute the given values.

${\sf \leadsto 6 = \dfrac{x + (2x - 8) + (2x + 2) + (3x - 1) + (4x + 1)}{5}}$

Add all variables and all constants together on numerator.

${\sf \leadsto 6 = \dfrac{12x - 6}{5}}$

Shift the denominator from RHS to LHS.

${\sf \leadsto 6 \times 5 = 12x - 6}$

Multiply the values on LHS.

${\sf \leadsto 30 = 12x - 6}$

Shift the number 6 from LHS to RHS, changing it's sign.

${\sf \leadsto 12x = 30 + 6}$

Add the values on RHS.

${\sf \leadsto 12x = 36}$

Shift the number 12 from LHS to RHS.

${\sf \leadsto x = \dfrac{36}{12}}$

Simplify the fraction to get the value of x.

${\sf \leadsto x = 3}$

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Now, let's find the value of each observation in the data.

Value of second observation :-

${\sf \leadsto 2x - 8}$

Substitute the value of x.

${\sf \leadsto 2(3) - 8 = 6 - 8}$

Subtract the values to get the value of second observation.

${\sf \leadsto (-2)}$

Value of third observation :-

${\sf \leadsto 2x + 2}$

Substitute the value of x.

${\sf \leadsto 2(3) + 2 = 6 + 2}$

Add the value sto get the value of third observation.

${\sf \leadsto 8}$

Value of fourth observation :-

${\sf \leadsto 3x - 1}$

Substitute the value of x.

${\sf \leadsto 3(3) - 1 = 9 - 1}$

Subtract the values to get the value of fourth observation.

${\sf \leadsto 8}$

Value of fifth observation :-

${\sf \leadsto 4x + 1}$

Substitute the value of x.

${\sf \leadsto 4(3) + 1 = 12 + 1}$

Add the values to get the value of fifth observation.

${\sf \leadsto 13}$

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Now, let's find the mode.

Mode :-

${\sf \leadsto 3, (-2), 8, 8, 13}$

As we can see that the number 8 had repeated two times as none had repeated. So,

${\sf \leadsto Mode = 8}$

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${\red{\underline{\boxed{\bf So, \: the \: correct \: answer \: is \: (Option \: 4) \: = 8.}}}}$