Question

Calculate the mean, median, and mode of the following set of data. round to the nearest tenth.

Answer 1

Given the following set:

`\lbrace14,2,15,15,2,1,5,7,11,6,2\rbrace`

we want to calculate the mean, the median and the mode.

The mean is the mathematical average of a set of two or more numbers. To calculate the mean we add all the elements in our set and divide by the amount of elements.

`\bar{x}=(\sum_i^nx_i)/(n)`

We have 11 elements in our dataset, therefore, the mean is:

`\bar{x}=(14+2+15+15+2+1+5+7+11+6+2)/(11)=(80)/(11)\approx7.3`

The mean is 7.3.

The median is the middle value when a data set is ordered from least to greatest. To calculate the median first we need to reorder our dataset in ascending order:

`\lbrace1,2,2,2,5,6,7,11,14,15,15\rbrace`

The median is the central number of a data set. Arrange data points from smallest to largest and locate the central number. This is the median. If there are 2 numbers in the middle, the median is the average of those 2 numbers. Since in our dataset we have an odd amount of elements, the median is just the middle value, which is 6.

The mode is the number in a data set that occurs most frequently. Count how many times each number occurs in the data set. The mode is the number with the highest tally. It's ok if there is more than one mode. And if all numbers occur the same number of times there is no mode.

In our dataset, the mode is 2(appears 3 times).

The answer is: mean = 7.3, median = 6, mode = 2.