http://www.ck12.org Chapter 1. An Introduction to Analyzing Statistical Data
This is not a hard and fast rule and is a good illustration of how many concepts in statistics are open to individual
interpretation. Some statisticians even say that the only correct answer to every question asked in statistics is, “it
depends”!
Weighted Mean
Theweighted meanis a method of calculating the mean when some of the data values are counted frequently. The
most common type of weight to use is thefrequency, which is the number of times each number is observed in the
data. The calculation gives the same result as the standard mean, but each observed data point is multiplied by its
weight first, then the total sum is calculated and the result is divided by the sum of the weights.
When we calculated the mean for the children living at home, we could have used a weighted mean calculation. The
calculation would look like this:
1 · 5 + 2 · 8 + 3 · 5 + 4 · 2 + 5 · 1 + 6 · 1
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Technology Note: Weighted Means on the TI 83 or 84 Graphing Calculator
Weighted means are easy to calculate using a graphing calculator. We can use listL1 for the number of children, and
in listL2 we will enter the frequencies, or weights.
Enter the data as shown in the left screen below:
For weighted means, we use the same procedure, but enter the two lists in the mean computation. Press[2nd]
’[LIST]’ to enter the list menu, press the left arrow[leftarrow]to go to the math menu (the middle screen above),
and either arrow down or choose 3 for the mean. Finally, press[2nd]Ω[comma]’[LIST]’[ ) ] [enter]and you will
see the screen on the right above. Note that the mean is 2.5, as before.
Percentiles and Quartiles
Apercentileis a statistic that identifies the percentage of the data that islessthan the given value. The most
commonly used percentile is the median. Because it is in the numeric middle of the data, half of the data is below
the median. Therefore, we could also call the median the 50thpercentile. A 40thpercentile would be a value in
which 40% of the numbers are less than that observation. Your first exposure to percentiles was most likely as a
baby! To check a child’s physical development, pediatricians use height and weight charts that help them to know
how the child compares to children of the same age. A child whose height is in the 70thpercentile is taller than 70%
of the children of their same age.
Two very commonly used percentiles are the 25thand 75thpercentiles. Because they divide the data into quarters
(when taken together with the median), they are referred to as thelower and upper quartiles. They are sometimes
abbreviatedQ 1 andQ 3. A quartile divides the data into 4 approximately equal groups. Technically, the median is a