Question

Hey guys! 40 points
question for uh all.
Find the mean, mode and median for the following :
1. 12,24,24,12,30,12
2.21,24,21,6,15,18,21,45,9,6,27 and 15.

Answer 1

Answer:

1. 19,18,12

2. 19,19.5,21

Step-by-step explanation:

(1)

Arrange the data in ascending order.

⇒ 12,12,12,24,24,30

Mean = Sum of observations/Total number of observations

         = (12 + 12 + 12 + 24 + 24 + 30)/6

         = 19.

Median = Total number of observations = 6{Even}

             = [(n/2) + (n/2 + 1)]/2

             = [(6/2) + (6/2+1)]/2

             = [3 + 4]th observation/2

             = 12 + 24/2

             = 18.

Mode = The element which occurs most number of times in the set.

          = 12.

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(2)

Arrange the data in ascending order

⇒ 6,6,9,15,15,18,21,21,21,24,27,45

Mean = (6 + 6 + 9 + 15 + 15 + 18 + 21 + 21 + 21 + 24 + 27 + 45)/12

         = 228/12

         = 19.

Median = [(n/2) + (n/2 + 1)]/2

             = ([6 + 7])th observation/2

             = (18 + 21)/2

             = 39/2

             = 19.5.

Mode = 21.

Hope it helps!

Answer 2

Hey there !!


▶ Question 1 .

→ 12, 24, 24, 12, 30, 12 .


▶ Solution :-

Firstly arrange the data in ascending order :

→ 12, 12, 12, 24, 24, 30 .


▶ Now,

$mean = \frac{sum \:ofobservations }{number \: of \: observation} . \\ \\ = \frac{12 + 12 + 12 + 24 + 24 + 30}{6} . \\ \\ = \frac{114}{6} . \\ \\ \huge \boxed{ \green{ = 19.}}$


▶ Median .

→ Total number of observations = 6 [ even ] .

$median = \frac{ (\frac{n}{2})th \: observation + ( \frac{n}{2} + 1)th \: observation }{2} . \\ \\ = \frac{( \frac{6}{2})th \: observation + ( \frac{6}{2} + 1)th \: observation}{2} . \\ \\ = \frac{3rd \: obsevation + 4th \: obsevation}{2} . \\ \\ = \frac{ 12+ 24}{2} . \\ \\ = \frac{36}{2} . \\ \\ = \huge \boxed{ \green{ = 18.}}$


▶ Mode :- Mode is that value of the variable at which the concentration of the data is maximum.

$mode = \huge \boxed{ \green{ = 12.}}$



▶ Question 2.

→ 21, 24, 21, 6, 15, 18, 21, 45, 9, 6, 27, 15.


▶ Solution :-

Arrange the data in ascending order :

→ 6, 6, 9, 15, 15, 18, 21, 21, 21, 24, 27, 45


▶ Now,


$mean = \frac{sum \:of \: observations }{number \: of \: observation} . \\ \\ = \frac{6 + 6 + 9 + 15 + 15 + 18 + 21 + 21 + 21 + 24 + 27 + 45}{12} . \\ \\ = \frac{228}{12} . \\ \\ \huge \boxed{ \pink{ = 19.}}$



▶ Median.

→ Total number of observations = 12 [ even ] .


$median = \frac{ (\frac{n}{2})th \: observation + ( \frac{n}{2} + 1)th \: observation }{2} . \\ \\ = \frac{( \frac{12}{2})th \: observation + ( \frac{12}{2} + 1)th \: observation}{2} . \\ \\ = \frac{6th \: obsevation + 7th \: obsevation}{2} . \\ \\ = \frac{ 18+ 21}{2} . \\ \\ = \frac{39}{2} . \\ \\ = \huge \boxed{ \pink{ = 19.5 \: .}}$


▶ Mode :- Mode is that value of the variable at which the concentration of the data is maximum.


$mode = \huge \boxed{ \pink{ = 21.}}$



✔✔ Hence, it is solved ✅✅.




THANKS




#BeBrainly.