Data simplification is effectively done by selecting a value known as an assumed mean. Assumed is a value chosen from the data set. It is subtracted from all other values to reduce the size of numbers in the data set.
An assumed mean is determined by selecting a number. This number is guessed as the mean among the values in the data set.
It is like picking one of the numbers in the dataset and assuming it is the mean for the data. By looking at the data, we can guess a number close to the mean. The mean is a measure of central tendency. It is most likely a number near the median of the data.
Take for instance the data set below.
89, 64, 56, 78, 88, 67, 72, 85, 70, 65, 64, 66, 72, 74, 76.
Arranging the data in ascending order we have
56, 64, 64, 65, 66, 67, 70, 72, 72, 74, 76, 78, 85, 88, 89.
Range= 89 – 56 =33
A method I find convenient to find a central data item is 56+(33/2) =56+17=73.
Now because we don’t have 73, I pick 72 as the assumed mean. And I will subtract 72 from each data item as in table below.
Now i get the summation of fd which gives ∑fd=-1
mean of x, x̄ = 72 + (-0.0667) = 71.9333
The sum of x has been done by a statistical software. Otherwise it is time consuming and error prone and energy sucking to try and compute it manually. It has been recorded there for comparison purposes.
in a more general case, if we take an assumed mean A and subtract it from each data item x, then we get data items labeled with d such that d=x-A and the mean for the data expressed as:
Practice question Data simplification
Using an assumed mean, calculate the mean of each of the following sets of data
(a)
0.655, 0.685, 0.705, 0.665, 0.695, 0.715, 0.375, 0.745, 0.755, 0.765, 0.745, 0.550, 0.450, 0.400, 0.425, 0.325, 0.775, 0.685, 0.695, 0.745
(b)
225, 400, 300, 225, , 525, 325, 600, 225, 325, 400,
525, 575, 625, 250, 650, 350, 475, 550, 575, 275,
375, 475, 475, 675, 400, 375, 275, 250.
Related Topics
- Introduction to statistics
- Measures of central tendency
- Easy Integration4: partial fractions
- Line graphs
- Bar graphs
- Grouped and un-grouped data
- Frequency Polygons
- Histograms
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