Question

Find the mean, median, and mode of the following set of data. (Enter solutions for mode from smallest to largest. If there are any unused answer boxes, enter NONE in the last boxes.) (a) 6 6 7 8 9 12 Mean Median Mode Mode (b) 6 6 7 8 9 108 Mean Median Mode Mode

Answer 1

a)

	X
	6
	6
	7
	8
	9
	12
Sum =	48

The sample mean is computed as follows:

In order to compute the median, the data needs to be put into ascending order, as shown in the table below

Position	X (Asc. Order)
1	6
2	6
3	7
4	8
5	9
6	12

Since the sample size n = 6 is even, we have that (n+1)/2 = (6+1)/2 = 3.5 is not an integer value, the median is computing by taking the average of the values at the positions 3th and 4th, as shown below

These are the sample data that have been provided:

XX

6

6

7

8

9

12

Based on the data shown above, we can construct the following table with the frequency (count) of each of the values in the sample:

X	Frequency (f)
6	2
7	1
8	1
9	1
12	1

Therefore, based on the information obtained about the number of times each value appears in the sample, it is concluded that the mode is 6, which is the value that is the most repeated.

b)

	X
	6
	6
	7
	8
	9
	108
Sum =	144

The sample mean computed as follows:

In order to compute the median, the data needs to be put into ascending order, as shown in the table below

Position	X (Asc. Order)
1	6
2	6
3	7
4	8
5	9
6	108

Since the sample size n = 6 is even, we have that (n+1)/2 = (6+1)/2 = 3.5 is not an integer value, the median is computing by taking the average of the values at the positions 3th and 4th, as shown below

These are the sample data that have been provided:

XX

6

6

7

8

9

108

Based on the data shown above, we can construct the following table with the frequency (count) of each of the values in the sample:

X	Frequency (f)
6	2
7	1
8	1
9	1
108	1

Therefore, based on the information obtained about the number of times each value appears in the sample, it is concluded that the mode is 6, which is the value that is the most repeated.