Calculate the correlation coefficient of the marks obtained by 12 students

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calculate the correlation coefficient of the marks obtained by 12 students

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LectureNotes said calculate the correlation coefficient of the marks obtained by 12 students

Answer:
To calculate the correlation coefficient (often referred to as Pearson’s correlation coefficient, denoted by r) for 12 students’ marks, you need pairs of values (for example, marks in two different subjects: Subject X and Subject Y). Follow the steps below:

  1. Assemble the Data: Create a table with each student’s scores in the two subjects.

  2. Compute Required Sums: Calculate:

    • \sum X (sum of X scores)
    • \sum Y (sum of Y scores)
    • \sum X^2 (sum of squares of X scores)
    • \sum Y^2 (sum of squares of Y scores)
    • \sum XY (sum of the product of X and Y for each student)

  3. Apply the Pearson’s Correlation Formula:

    r = \frac{n \sum XY - (\sum X)(\sum Y)}{\sqrt{\bigl[n \sum X^2 - (\sum X)^2\bigr]\bigl[n \sum Y^2 - (\sum Y)^2\bigr]}}

    Here, n is the number of pairs (in your case, 12).

  4. Interpret the Result:

    • r ranges between -1 and 1.
    • A value close to 1 indicates a strong positive correlation.
    • A value close to -1 indicates a strong negative correlation.
    • A value around 0 indicates no or very weak linear correlation.

Below is a sample table with hypothetical data for 12 students’ marks in two subjects (X and Y). You can replace the numbers with your actual data and follow the same process:

Student X (Subject 1) Y (Subject 2) X² Y² X·Y
1 65 70 4225 4900 4550
2 72 68 5184 4624 4896
3 81 78 6561 6084 6318
4 60 65 3600 4225 3900
5 90 88 8100 7744 7920
6 55 52 3025 2704 2860
7 74 80 5476 6400 5920
8 66 75 4356 5625 4950
9 78 85 6084 7225 6630
10 82 90 6724 8100 7380
11 58 60 3364 3600 3480
12 70 72 4900 5184 5040
  1. Calculate the sums (e.g., \sum X, \sum Y, \sum X^2, \sum Y^2, \sum XY).
  2. Plug them into the formula for r above.
  3. Obtain the correlation coefficient.

Key Points:

  • Always keep your data organized in a table to avoid mistakes.
  • Use precise arithmetic or software (like spreadsheet tools) to ensure accuracy.

Important: If you already have the summations (e.g., from LectureNotes), you can directly substitute them into the formula without rewriting the entire table.

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