What is LQ, UP, and IQ? Outlier? So confused?

Question

what...i was doing this math packet our 7th grade math teacher-to-be gave us over the summer, and came across something we didn't even learn about in sixth.

the set of data:
3,3,6,7,8,11,13,14,21,22,24

lower quartile? upper quartile? inter-quartile?
how do you determine if there is an outlier in a set of data?

*please explain answer thuroughly, do not just give the answer. and explain in a way that a 6yh/7th grader will understand.

thanks much! ...♥

Answer 1

http://sg.answers.yahoo.com/question/index?qid=20061025233049AAnctHz

http://www.dogpile.com/info.dogpl/search/web/What%252Bis%252Blower%252Bquartile%25253F/1/-/1/-/-/-/1/-/-/-/1/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/417/top/-/-/-/0

Answer 2

Quartiles are numbers that divide the data evenly into four subsets. The upper quartile cuts off the top quarter of the data from the rest. The bottom quartile cuts off the lowest quarter of the data from the rest. Additionally, the median which is the number right at the middle of the data, can be considered a quartile. Actually, I won't tell you anything that's not said in the wikipedia article below, which also includes an example very much like yours. So that's all I'll say about Quartiles.

Outliers as just data points that are a long ways away from the rest of the data. What it means to be "a long ways away" is somewhat open to debate, but it doesn't look to me like you data has an outlier. However, if you added an extra data point and instead had:

3,3,6,7,8,11,13,14,21,22,24, 10932890

then 10932890 would be an outlier.

Answer 3

Quartile simply means 1/4 or one-quarter of the whole set of data. In the case of your data, the first 1/4 of your data points lie in the first quartile, the second 1/4 of your data points are in the second quartile, etc. Naturally, there are four quartiles total in any data set.

You have N = 11 data points if I've counted correctly. Thus, 1/4 of 11 ~ 3, actually a bit under 3 but one cannot have a fraction of a data point.

Sorting your data points in ascending order, as you have already given them, the first 1/4 of them includes 3,3,6. Thus, they are the first quartile, which is your lower quartile because it contains the lowest values. The inner (two) quartiles consist of 7,8,11,13,14; leaving 21,22,24 in the upper one. We group 21 in the last quartile for obvious reasons; its value is closer to 22 than to 14.

An outlier is a data point that just doesn't fit in with all the others. They are easitly visible when the data values are mapped out on a bar graph for example. You can use your own data points to show this.

There are n(3-6) = 3 data points with values in the range 3 to 6. So we can draw a bar of length L(3-6) = 3 units lying on the interval (3-6).

There are n(7-10) = 2 data points with values in the range 7 to 10. So the bar length in the (7-10) range of data values would be L(7-10) = 2 units.

Similarly, n(11-14) = 3, n(15-18) = 0, n(19-22) = 2, and n(23-26) = 1. Thus, if you drew a bar for each range (e.g., 3 to 6 and 7 to 10), you find a maximum of 3 data points for the (3-6) and (11-14) ranges and a minimum of 0 data points for the (15-18) range of values. In sum, your bar graph would look like this:

(3-6....):XXX
(7-10..):XX
(11-14):XXX
(15-18):
(19-22):XX
(23-26):X

Looking at the bar graph, are there any ranges of value that seem to be out of place in your data? That is, is there a range of one or more values outside 3 through 26? No...not really. All eleven data points are grouped in that 23 = (26-3) interval of value. So your data points do not have outliers. (By the way, "outlier" literally means lies outside the normal range of values.)