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I'm trying to find the correlation between a categorical and numerical data by using google sheets. The result of CORREL function is 0.041.

Could anyone help how to proceed from here to understand if the correlation is meaningful?

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The correlation must be close to 1 for positive correlation, respectively -1 for negative correlation. A correlation whose coefficient is 0.041 is an insubstantial correlation.

Correlation coefficient:
< 0.1 Very small, negligible, insubstantial
0.1-0.3 Small, minor
0.3-0.5 Moderate, medium
0.5-0.7 Large, high, major
0.7-0.9 Very large, very high
0.9 > Almost perfectly, describes the relationship between two practically indistinguishable variables
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    $\begingroup$ Whether a correlation is "meaningful" depends on many things. No guidelines like this will be appropriate except in narrow circumstances. For instance, in many physical experiments a correlation of $99.99\%$ would be unacceptably low, whereas in some social sciences correlations around $20\%$ to $30\%$ would be outstanding and in financial applications any significant correlation, no matter how tiny, could be worth a small fortune. $\endgroup$
    – whuber
    Jul 5, 2022 at 20:51

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