Question

The mean of 2,3,5,1,7 and 6 is a. The numbers 3,5,4,2,3,7 also have mean a and median c. Find a and c.

Answer 1

Hint:
We will determine mean by adding the given numbers and dividing them by total number of terms. We will determine the median by arranging the numbers in ascending order and by taking the average of middle two terms.

Complete step by step solution:
Mean of 2, 3, 5, 1, 7 and 6 is a
 \[ \Rightarrow \] Mean \[ = \] (sum of all observations) \[ \div \] (Total number of observations)
 \[ \Rightarrow a = \dfrac{{2 + 3 + 5 + 1 + 7 + 6}}{6}\]
On adding values, we get
 \[ \Rightarrow a = \dfrac{{24}}{6}\]
On division we get,
 \[ \Rightarrow a = 4\]
Mean of 3,5,4,2,3 and 7 is also a
 Mean \[ = \] (sum of all observations) \[ \div \] (Total number of observations)
 \[ \Rightarrow Mean = \dfrac{{3 + 5 + 4 + 2 + 3 + 7}}{6}\]
So, we have
 \[ \Rightarrow a = 4\]
Median of 3,5,4,2,3 and 7 is c.
To determine median, we will arrange the numbers in ascending order and if there are an odd number of terms then median is the middle observation, if there is an even number of terms then the median is the average of the middle two terms.
First, we arrange the numbers in ascending order
i.e. 2,3,3,4,5,7
Median of 2,3,3,4,5,7 is
 \[ \Rightarrow c = \dfrac{{3 + 4}}{2}\]
So, we have
 \[ \Rightarrow c = 3.5\]

Hence value of a is 4 and that of c is 3.5

Note:
Arithmetic Mean: If we have the data set consisting of the values \[{a_1},{a_2},{a_3},...,{a_n}\], then the arithmetic mean A is defined by the formula:
 \[A = \dfrac{{{a_1} + {a_2} + {a_3} + ... + {a_n}}}{n}\]
Where n is the total number of terms.
Median: If we have the data set consisting of n values \[{a_1},{a_2},{a_3},...,{a_n}\], then first we will write them in ascending order.
If there are a total odd number of values, then median will be the middle term.
If there are a total even number of terms, then median will be the average of the two middle terms.