Question

If mean of 11, 15, 17, x + 1, 19, x -2 and 3 is 14, what is the mode?​

Answer 1

GIVEN :-

• mean of 11 , 15 , 17 , x - 2 and 3 is 14.

TO FIND :-

• The mode.

SOLUTION :-

$\dag \: \boxed{ \boxed{ \red{ \bf \: mean \: = \dfrac{sum \: of \: observation}{no. \: of \: observation}}}} \\ \\ \mapsto \sf \: 14 = \dfrac{11 + 15 + 17 + x + 1 + 19 + x - 2 + 3}{7} \\ \\ \mapsto \sf \: 14 = \dfrac{64 + 2x}{7} \\ \\ \mapsto \sf \: 14 \times 7 = 64 + 2x \\ \\ \mapsto \sf \: 98 = 64 + 2x \\ \\ \mapsto \sf \: 2x = 98 - 64 \\ \\ \mapsto \sf \: 2x = 34 \\ \\ \mapsto \sf \: x \: = \cancel \dfrac{34}{2} \\ \\ \mapsto \underline{ \boxed{ \blue{ \sf \:x = 17 }}}$

☛ Hence the value of x is 17.

☯ FOR MODE,

Mode :- Any which is occurred maximum Times is called mode.

◉ 11 ➟ 1

◉ 15 ➟ 1

◉ 17 ➟ 1

◉ x + 1 = 17 + 1 = 18 ➟ 1

◉ 19 ➟ 1

◉ x - 2 = 17 - 2 = 15 ➟ 1

◉ 3 ➟ 1

Here 15 occured maximum 2 times

∴ Mode = 15.

Answer 2

✴ Given :-

• If mean of 11, 15, 17, x + 1, 19, x -2 and 3 is 14.

✴ To Find :-

• Mode Of Observation.

✴ Solution :-

Formula For Mean :-

Mean = Sum Of Observations/Total Observations.

Put the values.

↣ 14 = 11 + 15 + 17 + x + 1 + 19 + x - 2 + 3/7.

↣ 14 = 64 + 2x/7.

↣ 14 × 7 = 64 + 2x.

↣ 98 = 64 + 2x.

↣ 2x = 34.

↣ x = 17.

So, The Observations Are :-

11,15,17,18,19,15,3

Now, Calculating Mode.

As 15 is coming most times (2), it is the mode.

Hence, Your Answer is 15.