Question

the mode of data set 8,8,8,8,8,..is​

Answer 1

Answer:

The answer is 6.

Let the 8 numbers be a1 <= a2 <= a3 <= … <= a8 (note that we don’t even need to employ the restriction to ‘whole numbers’ - we can prove this in full generality over the real numbers).

Then we are given that a1 = 2, and we wish to maximise a8, subject to the constraints on the mean, median and mode.

Since the median is 3, we have a4 + a5 = 6. But a5 >= a4, so a5 >= 3 (since adding a5 to both sides gives us that 2a5 >= a4 + a5 = 6).

Though, if a5 > 3, we would have that a4 = 6 - a5 < 3, and then it would be impossible for the mode to be 3 (since none of the numbers could be 3).

Hence, a5 = 3.

This, in turn, forces a4 to be 3.

Now, we have that a2 and a3 are at least 2, so a2 + a3 >= 4.

Moreover, we have that a6 and a7 are at least 3, so a6 + a7 >= 6.

Let S = a1 + a2 + a3 + … + a8.

Then, we have that S = 24, since the mean is 3, and the mean is S divided by 8 (so 3 = S/8 implies that S = 3•8 = 24).

Then S = 2 + a2 + a3 + 3 + 3 + a6 + a7 + a8 >= 2 + 4 + 6 + 6 + a8.

So S = 24 >= 18 + a8, so a8 <= 6.

So perhaps 6 is the maximum possible value of a8.

If we try the dataset 2, 2, 2, 3, 3, 3, 3, 6, we have a mode of 3, a sum of 6 + 12 + 6 = 24 (and hence a mean of 3), and a median of 3.

So, since a8 <= 6, and the fact that we have found a valid dataset with a8 = 6, we have maximised a8 and thus found the solution

Step-by-step explanation:

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Answer 2

8

Step-by-step explanation:

The mode is one of the measures of central tendency in a dataset. It is defined as the most recurring value in the dataset. Other measures of central tendency are median and mean or average.

Our dataset is 8,8,8,8,....so on.

All values in the dataset are therefore the same, i.e 8. The most recurring value therefore is also the same, 8.

It is thus, the mode of our dataset.