Question

Find the mean deviation (approximately) about
the mode for the following ungrouped data: 20,
25, 30, 18, 15, 40.​

Answer 1

Answer:

In working with data, there are several different ways to measure how closely grouped your data values are. The most common is the mean. Most people learn early in school to calculate the mean by finding the sum of a group of data values and then dividing by the number of values in the set. A more advanced calculation is the mean deviation about the mean. This calculation tells you how close to the mean your values are. Finding this consists of finding the mean for a data set, finding the difference of each data point from that mean, and then taking the mean of those differences.

Part 1

Calculating the Mean

   Image titled Calculate Mean Deviation About Mean (for Ungrouped Data) Step 1

   1

   Collect and count your data. For any set of data values, the mean is a measure of central value. Depending on the type of data, the mean tells you the central value of that data. To find the mean, you must first collect your data, either through an experiment of some sort or just from an assigned problem.[1]

       For this example, use the assigned data set of 6, 7, 10, 12, 13, 4, 8 and 12. This set is small enough to count by hand to find that there are eight numbers in the set.

       In statistical work, the variable N{\displaystyle N}N or n{\displaystyle n}n is commonly used to represent the number of data values.

   Image titled Calculate Mean Deviation About Mean (for Ungrouped Data) Step 2

   2

   Find the sum of the data values. The first step of finding the mean is calculating the sum of all the data points. In statistical notation, each value is generally represented by the variable x{\displaystyle x}x. The sum of all values is symbolized as Σx{\displaystyle \Sigma x}\Sigma x. The capital Greek letter sigma signifies finding the sum of the values. For this sample data set, the calculation is:[2]

       Σx=6+7+10+12+13+4+8+12=72{\displaystyle \Sigma x=6+7+10+12+13+4+8+12=72}\Sigma x=6+7+10+12+13+4+8+12=72

   Image titled Calculate Mean Deviation About Mean (for Ungrouped Data) Step 3

   3

   Divide to find the mean. Finally, divide the sum by the number of values. The Greek letter mu, μ{\displaystyle \mu }\mu , is commonly used to represent the mean. Therefore, the calculation of the mean is:[3]

       μ=ΣxN=728=9{\displaystyle \mu ={\frac {\Sigma x}{N}}={\frac {72}{8}}=9}\mu ={\frac {\Sigma x}{N}}={\frac {72}{8}}=9

Step-by-step explanation: