What sequence of 5 numbers have a mode of 7, mean of 9 and a median of 8?

There are 4 possible answers and they are:

This is assuming only integers are allowed.

Explanation:

The sequence starts off as {A,B,C,D,E}

The median is 8, which is the direct center (slot C).

So we can update the sequence to {A,B,8,D,E}

The mode is 7. The mode is the value that shows up the most frequent compared to the other values. This tells us that the mode must show up at least two times. In this case, it must show up exactly twice because of the A,B values which are smaller than the median 8 in slot C.

So we know that A = 7 and B = 7.

The sequence updates to {7,7,8,D,E} where D and E are not 7.

If either D and/or E were 7, then the list would be {7,7,7,8,x} or {7,7,7,7,8}; however, this would lead to the median not being 8. So this line of reasoning allows us to rule out neither D nor E being 7.

Let's add up those five values, and divide by n = 5, to compute the mean

mean = (A+B+C+D+E)/5

mean = (7+7+8+D+E)/5

mean = (22+D+E)/5

Set this equal to the given mean of 9 and isolate the D+E expression

(22+D+E)/5 = 9

22+D+E = 5*9

22+D+E = 45

D+E = 45-22

D+E = 23

Whatever D and E are, they add to 23.

Assuming D and E are integers, there are a few ways to have D+E result in 23. The further restriction is that neither D nor E can be smaller than 8. Refer to the last section.

Here are all of the integer solutions to D+E = 23 where D and E are 8 or larger.

There are 8 items in that list above. We can rule out the bottom half of that list because it repeats the top half (just in reverse order). Also, note how E is smaller than D in those items. We'll assume that D < E.

So we can shorten that list to

This leads to the four possible answers of:

This is assuming that only integers are allowed. If non-whole values are considered, then we'd have infinitely many possible answers. This is because there are infinitely many solutions to D+E = 23 where D and E aren't restricted to the integer values only.

introduction, methodology, results, discussion

step-by-step explanation:

an observational study is one which consists of actual observation to record data and then analyse the data.

there are a number of factors that should be analyzed before starting an observational study.

the main four factors are:

i) introduction:   this should be analysed to check whether the purpose of the study is correctly established and the data recorded are appropriate for the study

methodology:   the method of collecting the data, such as whether randomly selected, and whether sample size matches with the population to be studied, whether questions asked are easy to answer by common men, etc.

results: then results such as summary of data with comments should be studied thoroughly

discussion:   the last is the discussion, this can be either by management people or persons who are all interested , etc.

step-by-step explanation:

the true ones are a b and d