IB Mathematics Applications & Interpretation 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 $a\le 3a\le 5$.

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]