Question Type 2: Data given as parameters and finding the value of the data given some relationship/values of the central tendancy Exercises

In the arithmetic sequence of five terms $\{a, a+d, a+2d, a+3d, a+4d\}$, the second term is $10$ and the mean of the terms is $12$. Find the values of $a$ and $d$.

Given the set $\{2, 5, 7, a, 13\}$, the range is $11$. Find the possible values of $a$.

Given the data set $\{3,7,9,a,15\}$, the median is $9$ and the mean is $10$. Find $a$.

For the data set $\{3,5,a,12,15,18\}$, the median is $10$. Find $a$.

Given the data set $\{2,5,a,9\}$, the mean is $6$. Find $a$.

Given the ordered data set $\{1, 3, 5, a, 9, 11\}$, the median is $7$. Find $a$.

In the ordered data set $\{4,7,a,13,16\}$, the mean is equal to the median. Find $a$.

The data set $\{2,4,6,a,10,12,14,16\}$ has mean $9$. Find $a$.

For the data set $\{5,8,12,a,20,25\}$, the median is $14$. Find $a$.

The seven numbers $\{3,5,7,a,11,13,15\}$ have mean $9$. Find $a$.

In the set $\{2,4,6,10,13,a\}$, the mean is $7$. Find $a$.

The set $\{4, 8, 12, 16, a\}$ is arranged in ascending order. The mean of the set is equal to the median. Find the value of $a$.