Unit 4 Sec 3.2 Measuring location

Unit 4 Sec 3.2 Measuring location

11 December 2015

22:25

The most important and useful summary of dataset is a measure of its location, based on some sort of average or typical value. There is no signal and universal most appropriate of locations, but there are various useful measures   that can be chosen, depending on the situation and on the nature of the data. Each measure has its own pros and cons. The three most common measures of location in satatisties textbooks are the mean, the mode and the median.

  The mean which is often just called the average, is probably quite a familiar to you.

Strategy to find the mean

To find the mean of a set of numbers, add all the numbers together and divide by however many numbers there are in the set.

Example 1 Calculating the mean.

Find the mean of the texting times of the five teachers.

Solution

Add together the numbers in the “teacher times “dataset and divide by however many numbers are in the dataset

The mean is

(18+27+31+36+47)/5 = 159/5 = 31.8 seconds.

If so, you obtained a statistical average known as the median. Speaking roughly, the median is the data value that is in the middle when data are arranged in order. A more precise definition is

Strategy to find the median of a dataset.

To find the median of a set of numbers:

¨    Sort the data into increasing or decreasing order

¨    If there is an odd number of data values, the median is in the middle value.

¨    If there is an even number of data values, the median is defined as the mean of the middle two values.

Calculating the median is a lot easier if the data are already sorted. However, this too becomes a long calculation if you have to order a large set of values. So, for anything but the smallest set of data, it seems appropriate to turn to a calculator, spreadsheet or other software to compute these summary values. Fortunately, these are similar summary calculations can also be easily carried out using the dataplotter software.

Using Dataplotter to measure location

There are 4 types of plot available: Dotplot, Boxplot, Histogram and Scatterplot.

Dataplotter processes the information in two ways. First, the values are displayed visually as dotplots, a type of statistical plot where each data value is represented by the position of a dot along the number line below it. Dotplots area useful way of seeing patterns in data at a glance.

The second main outcome of selecting these datasets is that a set of ten key summary values has been automatically calculated and displayed for each dataset.