)The weights of 12 boys were measured in kg and the results are as follows: 39, 51, 38, 34, 29, 31, 42, 40, 52, 44, 41, 35 (i) What is the range of the data? (ii) What is the mean weight? (iii) What is the weight of the fattest boy? (iv) How many boys have weights more than the mean weights? Q.9) The number of family members of 17 families are as follows: 4, 3, 5, 2, 4, 6, 7, 3, 5, 2, 4, 4, 6, 5, 4, 2, 3. Find the mean, mode and median of this data. Q. 10) Find the median of the following data: i) 3, 5, 1, 2, 4, 6, 2, 2, 3 ii) 20, 23, 29, 21, 25, 27, 23, 30, 29, 24

Answer :

1 )  We have data  : 12 boys were measured in kg and the results are as follows: 39, 51, 38, 34, 29, 31, 42, 40, 52, 44, 41, 35  ,

First we write our data in ascending order , As :

29 , 31 , 34 ,35 ,38 , 39 , 40 , 41 , 42  , 44 , 51 , 52

i ) Range :  Range is difference between highest and lowest observation  . So

Range  =  ( 52  -  29 ) years  =  23 years

ii ) We know Mean  = Sum of all observationsNumber of observations , So

Mean weight = 29  +  31  +  34  + 35  + 38  +  39  +  40  +  41  +  42   +  44  +  51  +  52 12 = 47612 = 39.67 kg

iii )  Weight of fattest boy  =  52 kg                                                                                   ( Ans )

iv ) boys have weights more than the mean weight = 40 , 41 , 42  , 44 , 51 , 52 
So,
There are six boys have weights more than the mean weight .                                              ( Ans )

2 The number of family members of 17 families are as follows: 4, 3, 5, 2, 4, 6, 7, 3, 5, 2, 4, 4, 6, 5, 4, 2, 3.

First we write our data in ascending order , As :
2 , 2 , 2  , 3 , 3 , 3 , 4 , 4 , 4 , 4 , 4 , 5 , 5 , 5 , 6 , 6 , 7
So,
Mean  = 2  +  2  +  2   +  3  +  3  +  3  +  4  +  4  +  4  +  4  +  4  +  5  +  5  +  5  +  6  +  6  +  7 17 = 6917 = 4.058            ( Ans )

Mode :  The mode of a set of observations is the observation that occurs most often.
So,
Here mode  =   4   (  As 4 occurs more frequently )

Median : middle term is median of data , So

Here Median  = 4

3 )
i ) Median of data : 3, 5, 1, 2, 4, 6, 2, 2, 3 
First arrange given data in ascending order , As :

1 , 2 , 2 , 2 , 3 , 3 , 4 , 5 ,6 
So,
Median  =  3

ii ) Median of data : 20, 23, 29, 21, 25, 27, 23, 30, 29, 24 

First arrange given data in ascending order , As :

20 , 21 , 23 , 23 , 24 , 25 , 27 , 29 , 29 , 30 

Here we have even number of observation ( n  = 10 )  so 

We know Median  = n2th term + n2 + 1 th term 2
So,
Median  = 102th term + 102 + 1 th term 2 = 5th term + 6th term 2  = 24 + 252 = 492 = 24.5            ( Ans )
 

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I mean best of luck
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It's an easy question any 7th standard child can solve it I think you should try it beat of luck
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Range and of the data= 23kg Mean weight = 39.66kg. Weight of fattest boy =52kg. 6boys have more weight than mean weight
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