Answer:
i) 9
ii) 11
Explanation:
First off, what is a "mode"?
The mode in a set of data is simply the most common answer/outcome;
Next, we need to understand the data;
In this case, families were asked about the number of cats they have;
The children answered 0, 1, 2 or 3;
8 families have 0 cats,
6 have 1,
10 have 2,
x have 3
So, the mode will be the most common answer to how many cats a family has;
As we can see from the data, the most common response was 2, i.e. 10 families have 2 cats, compared to only 8 with 0 cats and 6 with 1 cat;
If we know the mode is 2, the value of x has to be less than 10 as it is not the most common response;
The largest possible value will be 9.
If the mode is 3, then that means the x has to be the greatest number of responses;
Since the greatest number of responses to the other options is 10, then the number of responses to having 3 cats has to be at least 11;
The smallest possible value of x, if the mode is 3, will be 11.