• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

Find out whether there is a correlation between the melting points and boiling points of the chemical elements.

Extracts from this document...


Bivariate Data Coursework


The aim of this investigation is to find out whether there is a correlation between the melting points and boiling points of the chemical elements. This idea is worth pursuing because it is related to my studies in A level chemistry and once data has been analysed the information would be useful to chemists for making predictions about the melting point or boiling point of an element if the other value is known. It is suspected that there will be positive correlation between the two variables because if a large amount of energy is needed to melt a solid it is likely that a large amount of energy will also be required to cause the liquid to boil and vice versa.

Data Collection

The population to collect data from will be all the elements in the periodic table of which there are about 118 that are known, and of these 50 will be selected randomly to collect data on. Both of the variables (melting and boiling point) are random, because they have unpredictable values and are free to assume any of a particular set of values in a given range. To select the 50 elements

...read more.


This is a technique used to calculate the correlation between two variables where there is a normal distribution; the value calculated always lies between 1 and –1 and is denoted by the letter r. A value of 1 means there is perfect positive correlation and –1 is perfect negative correlation. From looking at the scatter graph there appears to be a positive correlation so the value of r should be positive and near to 1.this technique takes into account the number of items of data and the spread within the data. The formula used is:

Sxy is the sample covariance and can be calculated using:

where x is the melting point and y is the boiling point. A spreadsheet has been used to calculate each total.

Sxx is a measure of the total square spread of the x values (melting points):

Syy is a measure of the total square spread of y values (boiling points):

r can then be calculated:

Since the correlation coefficient is 0.879, which is close to 1, there must be quite a strong positive correlation between the melting points and boiling points of the elements used in this sample.

Hypothesis Testing

To test whether the level of correlation calculated between the two variables is significant, a hypothesis test will be carried out.

...read more.


The main restriction of the findings are that although there is positive correlation between the two variables, there is no causation between melting points and boiling points so there must be some other factor in the structure of each element that determines these properties.

To improve the quality of results, a greater sample size should be used consisting of more elements, and the melting and boiling points could be found out more accurately from more reliable sources. This would make sure that the value of r calculated is more reliable. If a smaller significance level was used it would be possible to be more certain about whether there really is a positive correlation between melting and boiling points. So that predictions could be made about one variable if the other is known, a least squares regression line would need to be calculated to express the linear correlation algebraically.

...read more.

This student written piece of work is one of many that can be found in our AS and A Level Probability & Statistics section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related AS and A Level Probability & Statistics essays

  1. Is there a Correlation between GCSE Mathematics and English Literature scores?

    -0.5184 2 0 -1.52 -3.08 2.3104 9.4864 4.6816 7 8 3.48 4.92 12.1104 24.2064 17.1216 0 0 -3.52 -3.08 12.3904 9.4864 10.8416 1 1 -2.52 -2.08 6.3504 4.3264 5.2416 5 5 1.48 1.92 2.1904 3.6864 2.8416 4 2 0.48 -1.08 0.2304 1.1664 -0.5184 2 2 -1.52 -1.08 2.3104 1.1664 1.6416

  2. Driving test

    I can estimate the probability of passing or the probability of failing for each gender, with a certain instructor. I could also predict the average pass rate. With this method, my results will be far more accurate compared to just looking at the histograms.

  1. "The lengths of lines are easier to guess than angles. Also, that year 11's ...

    = 1 - 20965.5 = 1 - 1.066620879= -0.066620879 27(729 - 1) 19656 Therefore, this means that the spread of the year nine data will have almost no correlation at all when plotted on a scatter graph because if the Spearman's coefficient of rank is close to 1 then it means that the data will be strongly positively correlated.

  2. Estimating the length of the line and the size of the angle

    105.5 4 61.2 25 584 70 886 9 114.5 5 66.2 45 629 75 961 8.3 122.8 4.2 70.4 43 672 67 1028 10.3 133.1 7 77.4 45 717 55 1083 7.5 140.6 4.5 81.9 38 755 50 1133 10 150.6 5 86.9 50 805 70 1203 7.9 158.5 4.9

  1. I am investigating how well people estimate the length of a line and the ...

    12 36 45 12 36 45 12 36 45 12 36 45 12 36 20 13 39 20 13 39 49 16 48 15 18 55 60 27 82 60 27 82 65 32 97 Average Angle percentage error for Boys in year 7: 6 6 6 9 9 9

  2. Is there a correlation between happiness and sociability?

    "Happiness, along with health and mental health, is increased by presence of certain social relationships and depressed by those losing these..."(*6). This demonstrates how social relationships can not only affect a person's happiness, but also their health. Horowitz et al., 1982, and Weeks et al., 1980(*6)

  1. Mathematically Modelling Basketball Shots

    * The shots being taken from the same free-throw position which is fifteen feet away from the base of the net and perpendicular to the back line. * The same type of shot being used - using one hand to steady the ball and one to project the ball through the air.

  2. AS statistics coursework - correlation coefficient between height and weight in year 11 boys ...

    The linear equation that best describes the relationship between X and Y can be found by linear regression. The means by which I shall do this are as follows. I shall use the following equations further in my coursework in aid of finding correlation values.

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work