Question

Select all the statements that describe the following set of numbers.

3, 9, 8, 6, 3, 4, 9, 2, 5, 10, 8, 1
This set has three modes.
The median is the mean of 5 and 6.
The mean is smaller than the median.
The mode is 3.
The mean is approximately 5.67.

Answer 1

1,2,3,3,4,5,6,8,8,9,9,10

Median: 7


The mean is smaller han the meidan
The mean is approximately 5.66666667
This set has three modes.

Answer 2

Explanation:

The set of numbers is:

3,9,8,6,3,4,9,2,5,10,8,1

Arranging this set of numbers in the ascending order, we have

1,2,3,3,4,5,6,8,8,9,9,10

The mode is the number which occurs frequently in the set, therefore 3, 8 and 9 are the frequently occurring numbers in the given set, hence there are three modes in total.

The median is the middle number in the given data, since the numbers are even in nature, therefore the median will be the mean of the middle numbers that is:

Median=
`(5+6)/(2)`=
`(11)/(2)`=
`5.5`

Thus,the median is the mean of 5 and 6.

Mean=
`(1+2+3+3+4+5+6+8+8+9+9+10)/(12)`

=
`(68)/(12)`

=
`5.67`

Thus, mean is greater than the median.

Hence, The given set has three modes, the median is the mean of 5 and 6 and the mean is approximately 5.67.