Question

3. The following table shows the weight of 12 players:
Weight in kg 48 50 52 54 58
No. of players 4 3 2 2 1
Find the median and mean weights.
Using empirical formula, calculate its mode. [Note: Empirical formula for calculating mode is
Mode = 3 Median – 2 Mean]

Answer 1

Answer:

3) Weight of the players-............................................Number of Players

48 Kg................................................................................................4

50 Kg................................................................................................3

52 Kg................................................................................................2

54 Kg................................................................................................2

58 Kg................................................................................................1

Mean= Total Weight of Players/Total Number of Players.

Which Means, Mean=(48*4)+(50*3)+(52*2)+(54*2)+(58*1)/(4+3+2+2+1)

                   or Mean=(192+150+104+108+58)/12

                   or Mean=612/12

                   or Mean=51 Kg.

Mean= 51 Kg.

Let's Find the Median.

Step 1: Arrange the Data from Smallest to Greatest.

                       (48, 48, 48, 48, 50, 50, 50, 52, 52, 54, 54, 58)

Step 2:FInd out the Number of Data.

                       (48, 48, 48, 48, 50, 50, 50, 52, 52, 54, 54, 58)

Number of Datas: 12

Step 3: As the Number of Data is Even (12 is an Even Number), So the Median will be the Mean of the Two Middlemost Numbers.

                       (48, 48, 48, 48, 50, 50, 50, 52, 52, 54, 54, 58)

The Two Middlemost Numbers are 50 and 50.

Mean of 50 and 50= 50+50/2= 100/2= 50

Hence, Median Weight is 50 Kg.

Let's Find the Mode Using Empirical Formula.

Empirical Formula: Mode= 3Median- 2Mean

Let's Implement the Values.

Mode= (3*50)-(2*50)

or Mode= 150-100

or Mode= 50 Kg.

Hence, We Conclude,

Mean= 51 Kg

Median and Mode= 50 Kg.

Thanks.

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