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Question 1 Data Handling-Central Values Exercise 23.2

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.

Answer:

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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