Answer:
Range of x: [tex]0\leq x < 12[/tex] or [tex]0\leq x\leq 11[/tex]
Largest possible value of [tex]x[/tex] is 19
Mean mark = 11.41 (nearest hundredth)
Step-by-step explanation:
The mode is the number that appears the most, so if the mode is 10, [tex]x[/tex] has to be smaller than 10.
We can say this in two ways:
[tex]0\leq x < 12[/tex] or [tex]0\leq x\leq 11[/tex]
since the number of points and players are positive integers.
The median is the middle value when the values in the data set are placed in order from smallest to largest.
If 10 is the median mark, to find the maximum number of 15s, sum the number of players scoring 5 and 10 points and subtract 1:
8 + 11 = 19
Therefore, the largest possible value of [tex]x[/tex] is 19.
The mean is the total of the numbers divided by how many numbers there are.
To find the total marks, multiply the number of points by the number of players, and sum (using x = 19):
[tex]\textsf{Total points}=5 \times 8+10\times12+15 \times 19=445[/tex]
Total number of players = 8 + 12 + 19 = 39
[tex]\textsf{mean mark}=\dfrac{445}{39}=11.41\:\textsf{(nearest hundredth)}[/tex]
