Data handling - IQ correlation

* If your data requires you to use the mode as a measure of central tendency, you must use the range as your measure of dispersion. This only happens if you have to work with very simple data. The range is only dependent on the extreme values at either end of the data, so is not a very useful measure.

* The interquartile range is used when using the median as a measure of central tendency. Therefore if your data are not normally distributed (i.e. you have a skewed distribution) then the median and quartile deviation are probably the best way to measure it.

* When your data is normally distributed, then the mean and the standard deviation are the most best and most accurate measures.

The two latter processes are the most accurate, and these are the ones that I will be using throughout this investigation.

I will investigate hypothesis number 1 first (The lower the IQ of a person is, the more hours of TV that person will watch per week).

Firstly I have to remove all irrelevant data from my form. The only data that I have to include is "average number of hours of TV watched per week" and "IQ". In the below picture I am deleting irrelevant data.

This is what the spreadsheet will looks like now I have deleted all the irrelevant data- it only has the two data features that I am investigating. The sheet was divided into two groups (KS3 and KS4) so I combined the two groups.

I then sorted the data first into ascending order of IQ, then ascending order of "average number of hours of TV watched per week". I did this for two reasons- firstly if any data is invalid (for example if a person claims to watch 2500 hours of TV a week, this is obviously incorrect data, as there is only 168 hours in a week) then it can be easily found at the bottom or at the top of the list, and secondly, the data is sorted so it can be analysed more easily, e.g. the median, upper and lower quartiles, and the standard deviation can be calculated much easier. As I am doing most of the calculations using the computer, then really only the first reason applies, but it is still practical to sort the data.

The data that I have chosen to discount is IQ that is under 30 and over 170. Although it is possible for someone to get these scores, the average IQ is 100, so I have considered the evidence and decided to discount it, as the final result may be anomalous if I choose to include this data. Likewise, I have not only discounted data in the "hours of TV watched" column that claims over 168 hours (the number of hours in a week) of TV time but I have discounted data that is under 126 hours. The reason for this is that I have subtracted 6 hours of sleep for each night, as this is around the minimum sleep a person can survive on. Even if there is 168 hours in a week, no one could watch 168 hours of non-stop television.

When the data has been discounted, felt that it would be appropriate to draw a scatter graph for this data. A scatter graph is more suitable, because grouping the data would be much too difficult, and consequently drawing a box and whisker diagram would be to difficult with this variety of data. I will be looking for negative correlation between IQ and number of hours of TV watched, as my hypothesis was...

... 1. The lower the IQ of a person is, the more hours of TV that person will watch per week.

This is the graph that I have drawn.

This is the graph. It shows no correlation. The red line is the line of best fit, and this line is parallel with the x-axis. This means that there is no correlation between "IQ" and "Average Hours of TV watched per Week".

My hypothesis was "the lower the IQ of a person is, the more hours of TV that person will watch per week". My hypothesis was wrong. The conclusion I can draw from this is that:

. A person with a high IQ (according to the line of best fit) will watch the same amount of TV as a person with a low IQ.

2. The line of best fit is parallel to the x-axis, and its intercept is at 18.48. This means that the average amount of TV watched per week for any person is 18.48 hours or 18 hours 28 minutes and 7.5 seconds.

I will now examine my second hypothesis.

2.The older a person is, the higher that persons IQ is.

For this part of my investigation, I must group my data into ages. On the data sheet, the ages are divided up into years and months. I am going to disregard the month's column. The reason for this is that the data will have to be sorted into a manageable amount of groups, and the groups will be age in years, not age in year's months.

I will again need to remove all irrelevant data from the original form. The only data I will leave is "IQ" and "Age". This is the data sheet after I have removed all irrelevant data, and incorrect data. The incorrect data is an age that is less than 10 and more that 16, and an IQ that is below 30 and above 170 (these are the figures that I have used in my first hypothesis).

I have grouped my data into a chart, with all the information that I need.

This data is not normal/skewed, so I will use interquartile range and median as my measures of spread and central tendency.

Age

Median

Lower Quartile

Upper Quartile

Minimum score

Maximum score

Mean

Standard Deviation

1

01.5

99.75

06.25

88

28

02.6785

8.178805

2

02

98

07

68

34

01.8872

8.783175

3

02

99

07

69

32

02

9.161816

4

02

98

07

69

27

01.9186

9.419594

5

01

94

06

74

31

00.6402

9.498469

6

01

97

06

76

27

01.2420

9.078998

From this table I can see that the age group with the highest mean average is the 11 year olds. This single fact alone disproves my theory, but so that I can examine the statistics more closely, I will draw a box plot diagram from the results.

From this box plot diagram, I can tell that:

* The most consistent age group is the 11 year olds. They have the smallest interquartile range (6.5). They also have a median IQ of 101.5- 0.5 higher than the median for 15 and 16 year olds- disproving my hypothesis.

* The least consistent age group is the 15 year olds. They have an interquartile range of 12- nearly double that of the 11 year olds.

* Both the highest and lowest IQ comes from the 12 year olds.

* The 11, 12, 13 and 16 year olds all have a positive skew. The 14 year olds have normal distribution, and the 15 year olds have a slight negative skew.

My second hypothesis (The older a person is, the higher that persons IQ is) was wrong. The data above shows that there is no relation between age and IQ.

I will now investigate my third hypothesis:-

Males have higher IQs than females.

I will again discount incorrect data and delete data that is incorrect. I will ignore any gender other than male or female. I will discount any data in the IQ column that is <30 or >170. I will now modify my data sheet again.

To see if the data is skewed or un-skewed, I will draw a frequency curve. I am doing this to help me decide which measures of central tendency and dispersion to use. (If the data is skewed, I will use median and interquartile range, if not I will use mean and standard deviation).

This data is not skewed, so I will use standard deviation and mean as my methods of measure.

Gender

Mean

Standard Deviation

Lowest IQ

Highest IQ

Male

01.3289

9.345069578

68

34

Female

01.9878

8.939091418

69

32

The female mean is slightly higher than the males, which proves my hypothesis wrong once again. Also, the males have a larger standard deviation, which means that the spread of data is bigger in the males, meaning that they are less consistent than their female counterparts. However, if you look at the above frequency graph, and also look at the