STATISTICS

Lauran Sparke &

Shano Zeelie

STATISTICS EVERYWHERE!!!!

What is statistics?• a branch of mathematics that provides techniques to

analyze whether or not your data is significant

(meaningful)

• Statistical applications are based on probability

statements

• Nothing is “proved” with statistics

• Statistics are reported

• Statistics report the probability that similar results

would occur if you repeated the experiment

It can be simple…

The results of learners in the class after writing a test out of 50

25, 30, 15, 21, 23, 33, 23, 25, 40, 41, 37, 26, 39, 50, 10, 23, 23, 34, 16, 19, 42, 39, 20, 21

Step 1: Rearrange it from the lowest to the highest

10, 15, 16, 19, 20, 21, 21, 23, 23, 23, 23, 25, 25, 26, 30, 33, 34, 37, 39, 39, 40, 41, 42, 50

Mean – the sum of all the values in a data set divided by the total number of

values in the data set. Median – middle-most value in the data set when the values are arranged in ascending or descending order.Mode – value that occurs most in the data

set.

10, 15, 16, 19, 20, 21, 21, 23, 23, 23, 23, 25, 25, 26, 30, 33, 34, 37, 39, 39, 40, 41, 42, 50

Mean – 28,125

Median – 25

Mode - 23

A five point summary starts with the lowest value in the data set.

Quartile 1 - the middle number between the smallest number and the median of the data set. 

Median Quartile 3 – the middle value between the

median and the highest value of the data set. Highest number -

5 point summary of the data

5 point summary of the data

Lowest – 10 Quartile 1 – 21 Median – 25 Quartile 3 – 38 Highest – 50

But here is where it gets tricky…In a series of data we will sometimes find what we call “outliers”. This refers to the value or object that is either a lot more than the mean or a lot less than the mean. This can be calculated using standard deviation.

Normal curve and standard deviation

When we look at the shoe sizes of women we can say that the average shoe size is between a size 5 and a size 7 shoe. So we can say that the mean is a size 6. Now the outliers in this situation will probably be women with a size 3 and a size 12 shoe.

1 2 3 4 5 6 7 8 9 10 11 12

mean

Outliers Outliers

In this case the outliers refers to shoe sizes for women that we rarely find. There are not many women that wear a size 2 or a size 12 shoe and therefore it can be referred to as an outlier.

If it lies right of the mean then it is a lot higher than the mean and when it lies left of the mean the value is a lot less.

We read about and see statistics on a regular basis all around the world. But what is

important to remember is that in many cases statistics

can be very misleading.

Understanding statistics

Advertisements often make use of statistics without giving us any values or details.

Example 1In the Sensodyne toothpaste advertisement they specify that is it recommended by most dentists. This causes the public to believe that most dentists in South Africa recommends it, but the question is how many dentists were asked?

It could be that only 10 dentists were asked which is not the majority.

Let’s take a look at more examples…Example 2

Let’s imagine that you are searching for a job.

Company one offers you a 5% increase of your monthly salary every year and Company two offers you a 15% increase of your monthly salary every year.

It sound like 15% is a much better offer than that of 5% but the question is 15% of what?

Let’s imagine that the monthly salary of company one is R30 000

And the monthly salary of company two is R10 000

Company two looks much more appealing because it is 15% increase but in this case it is 15% of a much lower salary

Company one

5% of R30 000 = R1500

Company two

15% of R9000 = R1350

Example 3

In my medical aid contract it states that it will cover 100% of certain surgeon costs, but what it doesn’t state is that many surgeons charge 150% or 200% of the costs. To me 100% seems like the full payment and therefore it is misleading

It is easy to misinterpret some statistics when details are left out and therefore we should always do more research before we make any decisions.