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The phrase "analysis of the variations" is correct and usable in written English.
It can be used in contexts where you are discussing the examination or study of differences or changes in data, results, or phenomena.
Example: "The analysis of the variations in temperature over the past decade reveals significant climate trends."
Alternatives: "examination of the differences" or "study of the changes".
Exact(18)
Analysis of the variations of HIV-1 viral load (VL) in a cohort of patients.
This paper presents the results of an analysis of the variations of the scale height at the F2-layer peak (Hm) under different seasonal and solar-activity conditions.
First, a thorough graphical analysis of the variations in the maximum amplitude magnification factor depending on two design parameters, natural frequency and absorber damping ratios, is performed.
Global media coverage of her upcoming work will assuredly contain analysis of the variations in her clothes, her hair colour and her body language with her husband of eight years, country-music singer Keith Urban.
Many studies have dealt with an analysis of the variations of Hm in recent years (e.g. Belehaki et al., 2006; Zhang et al., 2006; Lee and Reinisch, 2007; Mosert et al., 2007; Nambala et al., 2008).
This paper presents a preliminary analysis of the variations of the critical frequency of the F2 region (foF2) and the total electron content (TEC) derived from Global Positioning System (GPS) data.
Similar(42)
A separate analysis of the variation in crime trends published on Thursday by the ONS shows a 41% drop in crime between 2002-03 and 2011-12 for police recorded crime figures, compared with a 26% drop in the crime survey results over the same period.
Table 10 Effect size analysis of the variation in the percentage of urban population.
These are explained on the basis of a Fourier analysis of the variation in the elastic properties around the ring.
We use earlier developed method of LLBL thickness determination based on the analysis of the variation of plasma velocity in the layer perpendicular to the magnetopause.
The analysis of the variation of the Walden product with solvent composition indicates an enhancement of the solvent structure in the water-rich region.
More suggestions(16)
analysis of the deviations
analysis of the mutations
assessment of the variations
analysis of the alternatives
analysis of the varied
analysis of the variability
analyses of the variations
analysis of the variant
analysis of the variance
analysis of the discrepancy
analysis of the alternative
analysis of the interviews
analysis of the politics
analysis of the data
analysis of the personnel
analysis of the results
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com