All Junior Cert Mathematics posts
• Higher maths paper 2 statistics Insa333

Can anyone give me a good guide to describing the distribution of data, i.e, skewed distribution, outliers, etc...... I really don't understand what they mean. "HELP"...........

1. Dazzla16

The distribution of data is how data is spread out.

If you look at histograms (you will find examples in any maths textbook), the bars will be distributed in some way.

You will notice that some data represented in histograms are balanced and some are skewed.

A balanced distribution is where the highest bar in the histogram is exactly in the middle.

A skewed histogram is where the highest bar is not in the middle.

-A positive skew is where most of the data is at the lower values i.e. left of the histogram

-A negative skew is where most of the data is at the higher values i.e. right of the histogram

Here are line plots to illustrate each of these:

Balanced:

..

....

........

..........

Positive skew:

...

.....

................

...........................

Negative skew:

..

.....

.................

.......................

An outlier is an extreme value in data that can affect the mean (a type of average) of the data

For example: these are the marks a class got out of 100 in a maths test:

26 28 30 32 34 36

Mean: 26+28+30+32+34+36

__________________ = 31

6

Since there is no outlier, the mean is not affected and as you see, the mean is very representative of the marks received by the whole class.

Now let's add an extreme value to the data (let's say an additional student was counted, and he got 94 marks)

26 28 30 32 34 36 94

Mean: 26+28+30+32+34+36+94

_____________________ = 40

7

Look what the outlier has done. The mean has dramatically increased to 40. This is not representative of the marks received by the whole class, because 6/7 students (the majority) didn't even reach 40.

I hope this helps, and if you have more questions, please ask! I am an A-grade 3rd year student in maths, and I am here to help anyone in maths!

2. Dazzla16

I'm sorry for how the line plot turned out. I did put spaces, but somehow it didn't work. I hope you understand what I mean by positive and negative skew.

3. Insa333

This is the best explanation anyone has given me so far on this topic, thank you so much for taking your time out, I really appreciate it!

4. Dazzla16

No problem :)

5. Me

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