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Data Handling-Central Values | Data Handling-Central Values Exercise 23.2

Question 1

A die was thrown 20 times and the following scores were recorded: 5, 2, 1, 3, 4, 4, 5, 6, 2, 2, 4, 5, 5, 6, 2, 2, 4, 5, 5, 1. Prepare the frequency table of the scores on the upper face of the die and find the mean score.

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  • Solution

  • Transcript

The frequency table for the given data is as follows:

X: 1 2 3 4 5 6
Y: 2 5 1 4 6 2

To compute arithmetic mean we have to prepare the following table:

Scores(Xi) Frequency(fi) Xifi
1 2 2
2 5 10
3 1 3
4 4 16
5 6 30
6 2 12
Total 20 73

Mean score = Σ fi xi/ Σ fi

= 73/20

= 3.65

"hello students welcome to leader learning india's best online classroom our question for today is we need to solve these two given equation so let's solve the first part of the given equation which is given x x minus 1 upon x plus 1 is equals to 2 x minus 5 upon 3 x minus 7 now if we cross multiply this we will get it as x minus 1 multiplied by 3x minus 7 will be equals to 2x minus 5 and x plus 1. correct so now if we solve this it will be open the bracket and multiply the values we will get it as 3 x squared minus 7x minus 3x plus 7 is equals to 2 x squared plus 2x minus 5x minus 5. so now if we rearrange this equation we will get it as x square minus 7x plus 12 is equals to zero now if we break this seven we will get the value as x square minus 4x minus 3x plus 12 is equals to 0 solving this we will get the value as x minus 4 x minus 3 is equal to 0 so if x minus 4 is equals to 0 it implies that value of x is equals to 4 and if x minus 3 is equals to 0 it implies that value of x is equal to 3 and these are the two values of x for the first given equation now let's solve the second equation second equation says that 1 upon x plus 2 plus 1 upon x is equals to 3 upon 4 if we take lcm it will comes out to be x into x plus 2 and here we will be having x x plus 2 value is again equals to 3 by 4 so the value will be equals to 2 x plus 2 now we if we cross multiply this simultaneously we will get 4 here and 3 multiplied by x multiplied by x plus 2 open the brackets all this solve the equation 4 x 2 is 8 x plus 8 is equals to 3 x multiplied by x comes out to be 3 x square plus 6 x the equation we get from here is 3 3x square minus 2x minus 8 is equals to 0. let's divide this value 2 into values so that the multiplication will be minus 8 and 3 that is 24 so we are dividing this value of minus 2 as minus 6x plus 4x minus 8 is equals to 0 all right so now let's take common 3x x minus 2 here will be common minus 4 sorry plus 4 x minus 2 it will be common again okay so the value is 3x plus 4 x minus 2 is equals to 0 now if we take 3x plus 4 is equal to 0 then it implies that value of x is minus 3 upon 4 and if x minus 2 is equals to 0 it implies that value of x is equals to 2 so here we get the we again get the two values of x 1 is x equals to minus three by four and another one is x equals to two so i hope that all your doubts are now cleared for more questions do subscribe leader learning thank you so much"

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subject-cta

Question 1

A die was thrown 20 times and the following scores were recorded: 5, 2, 1, 3, 4, 4, 5, 6, 2, 2, 4, 5, 5, 6, 2, 2, 4, 5, 5, 1. Prepare the frequency table of the scores on the upper face of the die and find the mean score.

  • Solution

  • Transcript

The frequency table for the given data is as follows:

X: 1 2 3 4 5 6
Y: 2 5 1 4 6 2

To compute arithmetic mean we have to prepare the following table:

Scores(Xi) Frequency(fi) Xifi
1 2 2
2 5 10
3 1 3
4 4 16
5 6 30
6 2 12
Total 20 73

Mean score = Σ fi xi/ Σ fi

= 73/20

= 3.65

"hello students welcome to leader learning india's best online classroom our question for today is we need to solve these two given equation so let's solve the first part of the given equation which is given x x minus 1 upon x plus 1 is equals to 2 x minus 5 upon 3 x minus 7 now if we cross multiply this we will get it as x minus 1 multiplied by 3x minus 7 will be equals to 2x minus 5 and x plus 1. correct so now if we solve this it will be open the bracket and multiply the values we will get it as 3 x squared minus 7x minus 3x plus 7 is equals to 2 x squared plus 2x minus 5x minus 5. so now if we rearrange this equation we will get it as x square minus 7x plus 12 is equals to zero now if we break this seven we will get the value as x square minus 4x minus 3x plus 12 is equals to 0 solving this we will get the value as x minus 4 x minus 3 is equal to 0 so if x minus 4 is equals to 0 it implies that value of x is equals to 4 and if x minus 3 is equals to 0 it implies that value of x is equal to 3 and these are the two values of x for the first given equation now let's solve the second equation second equation says that 1 upon x plus 2 plus 1 upon x is equals to 3 upon 4 if we take lcm it will comes out to be x into x plus 2 and here we will be having x x plus 2 value is again equals to 3 by 4 so the value will be equals to 2 x plus 2 now we if we cross multiply this simultaneously we will get 4 here and 3 multiplied by x multiplied by x plus 2 open the brackets all this solve the equation 4 x 2 is 8 x plus 8 is equals to 3 x multiplied by x comes out to be 3 x square plus 6 x the equation we get from here is 3 3x square minus 2x minus 8 is equals to 0. let's divide this value 2 into values so that the multiplication will be minus 8 and 3 that is 24 so we are dividing this value of minus 2 as minus 6x plus 4x minus 8 is equals to 0 all right so now let's take common 3x x minus 2 here will be common minus 4 sorry plus 4 x minus 2 it will be common again okay so the value is 3x plus 4 x minus 2 is equals to 0 now if we take 3x plus 4 is equal to 0 then it implies that value of x is minus 3 upon 4 and if x minus 2 is equals to 0 it implies that value of x is equals to 2 so here we get the we again get the two values of x 1 is x equals to minus three by four and another one is x equals to two so i hope that all your doubts are now cleared for more questions do subscribe leader learning thank you so much"

Our top 5% students will be awarded a special scholarship to Lido.

subject-cta
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