Question

the mean of 1,7,5,3,4and4 is m. the numbers 3,2,4,2,3,3,and p have a mean equal to m-1 and median q. Find the value of p and q.

Answer 1

Answer:

Value of p = 4

Value of q = 3

Step-by-step explanation:

It is given that the mean of 1 , 7 , 5 , 3 , 4 and 4 is m .

We know ( formula ),

Mean = ( sum of observations ) / ( number of observations )

Therefore,

= >  m = ( 1 + 7 + 5 + 3 + 4 + 4 ) / 6

= >  m = 24 / 6

= >  m = 4

It is given in the question that the mean of other numbers is m - 1,

So,

= >  m - 1 = ( 3 + 2 + 4 + 2 + 3 + 3 + p ) / 7

= > ( 4 - 1 ) 7 = 17 + p

= >  21 - 17 = p

= > 4 = p

Given : q is the median of 3 , 2 , 4 , 2 , 3 , 3 , and p( i.e 3 ).

Firstly, arranging the given numbers in ascending / descending order.

⇒ 2 , 2 , 3 , 3 , 3 , 3 ( which is p ) , 4

Median = ( n + 1 ) / 2 th term

             = ( 7 + 1 ) / 2 th term

             = 8 / 2 th term

            = 4 th term

            = 3

Therefore,

Value of p is 4. Value of q is 3

Answer 2

Answer : m = 4 , p = 4 and q = 3

Solution :
_________

Given that :

The mean of observation 1,7,5,3,4,4 = m

As we know that :

$mean = \frac{sum \: of \: observations}{no \: of \: observation}$

According to the question :

$m = \frac{1 + 7 + 5 + 3 + 4 + 4}{6} \\ \\ = > m = \frac{24}{6} = 4$

So, the value of m will be 4

Also given that : the mean of observation 3,2,4,2,3,3,p is m-1

According to the question :

$m - 1 = \frac{3 + 2 + 4 + 2 + 3 + 3 + p}{7} \\ \\ = > m - 1 = \frac{17 + p}{7} \\ \\ = > 4 - 1 = \frac{17 + p}{7} \\ \\ = > 3 = \frac{17 + p}{7} \\ \\ = > 21 = 17 + p \\ \\ = > p = 4$

So, with the value of p = 4 the observations will be 3,2,4,2,3,3,4

Given that the median of this observation is q.

As we know that from the definition of "Median" that when observation is in the form of ascending or descending then mid point of observation is called median of the observations.

Now, on rewrite the observations in ascending order :

2,2,3,3,3,4,4

Median = q = (n+1)/2 th term

Median = q = (7+1)/2 = 4th term

Median = q = 3

So, the value of q will be 3