Question

State whether the following statement is true or false:
The data 6, 4, 3, 8, 9, 12, 13, 9 has a mean of 9.

Answer 1

Hint: First, we will get to know the meaning of mean and its formula for a clear picture and then put in the values to obtain and match it with 9. If they do match, then the statement is true.

Complete step-by-step answer:
Let us firstly get to know the meaning of Mean.
The mean is the average of the numbers. The term 'average' refers to the 'middle' or 'central' point. Its formula is given by the sum of all the data divided by the frequency of the given data.
So, here, we have given numbers which are 6, 4, 3, 8, 9, 12, 13, 9.
To put in the formula, we need the sum of all these numbers.
Sum = 6 + 4 + 3 + 8 + 9 + 12 + 13 + 9
So, the sum of numbers will be = 64.
We see that we have data of 8 numbers.
So, frequency of data = 8.
So, now we will use the formula of mean which is the sum of all the data divided by the frequency of the given data.
So, $Mean = \dfrac{{64}}{8}$.
We can write it as: $Mean = \dfrac{{8 \times 8}}{8} = 1 \times 8 = 8$.
Hence, the mean is 8.
But in the statement we have: The data 6, 4, 3, 8, 9, 12, 13, 9 has a mean of 9.
Hence, the given statement is false.

Note: The students might make the mistake of reading the question hurriedly or something like.
For example:- State whether the following statement is true or false:
The data 6, 4, 3, 8, 9, 12, 13, 9 does not have a mean of 9.
Then its answer will be definitely true.
The student might get confused with the term “middle” or “central” but collectively seeing the whole and finding the middle number is the average.