Question

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Answer 1

Mean=13.22

Median=13.05

Standar deviation=3.51

• The mean is a measure of central tendency in a probabilistic sense. Matematically speaking, it can be calculated as the average of the elements that conform a set of numbers. It is important because it provides you with information about a dataset without having to know every value of your data. As an example, if you have a sample of the age of school teachers, the mean age of teachers will tell you what is the average age among all the teachers in the sample.It can be calculated like this:
  `(1)/(n) * \sum x = (1)/(n) * (12+12.5+18.2+13.6+15.3+7.7) = 13.22`
• The median value results from ordering the dataset in an ascending way, from the smallest to the greatest, and then determining which value divides the sample ordered in this way, in half. It is an other measure of central tendency and it helps you to know about the balance of your data. In the example provided before, if the median age of teachers is 45, you know that half of teachers are older than 45, and the other half is younger. When dealing with a finite set of numbers, the median’s value will depend on the characteristic of the sample. If there is an odd number of observations, the median value will be the middle value. On the other hand, if there is an even number of observations, the median will be the average between the two middle values. In the exercise, this value is calculated as the average between 12.5 and 13.6, which results in 13.05.
• Standar deviation is a measure of dispersion around the mean value. Its value is an indicator of how near are the observations in the sample, from the mean. A low standard deviation imply that the observations in your dataset are closed to the mean value. In terms of the teachers’ example, if the mean is 50 and the standard deviation is 2, many of the teachers in your datasets are between 48-52 years old. Following this example, if the standard deviation was 10 and the mean 50, most of the teachers would be between 40 and 60 years old (mean plus and less 10 years). The lowest the standard deviation, the more informative the mean: when the standard deviation is small, the values of the sample are closer to the mean. To obtain the standar deviation value one should use the following equation:
  `s=\sqrt{(1)/(n-1) * \sum{ (x_(i) - \bar{x})^(2) } \\`, where
  `\bar{x}` is the mean value that you calculated before, and "n" is the number of observations in the sample.