Math Problem Statement

A researcher is interested in whether the variation in the size of human beings is proportional throughout each part of the human. To partly answer this question they looked at the correlation between the foot length (in millimeters) and height (in centimeters) of 30 randomly selected adult males. The data is provided below. Use Excel to calculate the correlation coefficient r between the two data sets. Round your answer to two decimal places. Foot length (mm) Height length (cm)

240.2 199.9

241.3 198.9

242.5 197.9

243.8 196.9

244.9 195.9

255.3 194.9

256.9 194.9

257.1 193.9

258.4 192.9

259.6 191.9

260.1 189.9

216.7 188.9

262.3 187.9

264.4 186.9

265.3 185.9

266.5 184.9

226.7 183.9

257.8 182.9

268.9 181.9

269.1 161.9

270.9 162.9

236.7 163.9

271.8 164.9

273.9 165.9

274.7 166.9

275.3 167.9

246.7 168.9

279.6 169.9

280.1 141.9

281.9 142.9

Solution

To calculate the correlation coefficient rr between the foot length and height, you'll need to use Excel’s CORREL function, which computes the Pearson correlation coefficient. Here's a step-by-step guide on how to do that:

Steps to calculate the correlation coefficient in Excel:

  1. Enter the Data:

    • Open Excel and create two columns: one for foot length (mm) and the other for height (cm).
    • Enter the data in the respective columns.
  2. Use the CORREL Function:

    • Click on an empty cell where you want to display the correlation coefficient.

    • Type the following formula:

      =CORREL(A2:A31, B2:B31)
      

      Explanation:

      • A2:A31 is the range where the foot length data is entered.
      • B2:B31 is the range where the height data is entered.
  3. Press Enter:

    • After typing the formula, press Enter. The result will give you the Pearson correlation coefficient rr.

Result:

Once you apply the formula, Excel will provide the correlation coefficient. You can then round it to two decimal places as required.

Let me know if you'd like any further clarification or if you need assistance with anything else!

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Math Problem Analysis

Mathematical Concepts

Correlation
Statistics
Pearson correlation coefficient

Formulas

Pearson correlation coefficient formula: r = Σ[(Xi - X̄)(Yi - Ŷ)] / √[Σ(Xi - X̄)² Σ(Yi - Ŷ)²]

Theorems

Pearson correlation theorem

Suitable Grade Level

Grades 10-12