Statistics

Statistics

Let us look at an example! We are given the following data set of student ages in the general statistics class. You are asked to calculate the mean of our given population.

Student ages: 31, 33, 30, 31, 35, 33, 36, 28, 42, 37, 33

For the 1 st step, we need to find the sum of the observations. To do this, we simply add all the ages together.

31 + 33 + 30 + 31 + 35 + 33 + 36 + 28 + 42 + 37 + 33 = 369

369 is the sum of all the observations, or the sum total of all of the student’s ages in our example population. Right now this number does not tell us a lot of information, so we need to move on to step 2.

For the 2nd step, we need to determine the number of observations in the data set. For our example, we have 11 students in the class, so 11 is our number of observations. Now, we can solve for the mean by taking 369 / 11 which gives us an average class age of 33.5 years you could round this number up to 34 years.

*Important Points!

• Many times, you will be asked to calculate the average. Remember, the average is the same as the mean. • The number of observations can also be written as . The letter is just shorthand to denote the number of observations in a given data set or population. • The / symbol stands for division. *Questions to think about: Why is it important to study the mean of a population? What useful information can the mean give use about a given population? Median : The median is the middle value or number to a given set of numbers placed in order from smallest to largest. The median can be used to separate the data set into lower and upper values. The median is easily identified in number sets with an un-even amount of values. For example, in a number set with 15 values, the median can be identified by counting equally from each end. The median would be the 8th value. In even number sets, the median is calculated by adding the two middle values and dividing by two.

Let us look at our previous data set to determine the median.

Student ages: 31, 33, 30, 31, 35, 33, 36, 28, 42, 37, 33

The 1st step is to place the data set in order from smallest value to the largest value.

28, 30, 31, 31, 33, 33, 33, 35, 36, 37, 42

*Tip: Sometimes it is helpful to cross out the numbers as you place them in order – always go back and count to make sure you have included all of the values!

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