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

For the data set $\{3, 5, 7, a, 11, 13\}$, the median is $8$. Find the value of $a$.

In the eight-term set $\{2, 4, 6, a, 10, 12, 14, 16\}$, the median is 9 and the mean is 9. Find the value of $a$.

Let the data set be $\{a, 3a, 5, 7, 9\}$. If the mean equals the median, find the value of $a$, assuming $a ≤ 3a ≤ 5$.

In the list $\{4, 8, 12, a, 16\}$, the median is equal to 10. Find the value of $a$.

Let the six consecutive terms of a sequence be $\{x, x+2, x+4, x+6, x+8, x+10\}$. If the median of these terms is 8, find $x$.

The following numbers are listed in increasing order: $12, 15, a, 21, 24, 27, 30$. The mean of these seven numbers is equal to their median. Find the value of $a$.

Find $a$ if the eight-term set $\{2, 5, 8, a, 11, 14, 17, 20\}$ has mean 10.

For the data set $\{2, 5, a, 9, 12\}$, the mean is twice the median. Determine the value of $a$.

In the data set $\{1, 4, 10, 13, a\}$, find the value of $a$ such that the mode is 10.

In the set $\{6, 8, 10, 12, a, 16\}$, the mean is $11$. Find the value of $a$.

Given the data set $\{3, 7, a\}$ with mean 6, find the value of $a$.

Given that the set $\{a, 3, 5, 7, 9, 11, 13\}$ has a mean of 7, determine the value of $a$. [2 marks]