Question

the mean mathematics achievement test score of one section of first year high school students is 55 with a standard deviation of 15. in another section in the same school, the mean is 30 and the standard deviation is 10. what are the coefficients of variation of the two sections? 18.33% and 25.87% 27.27% and 33.33% 11.10% and 21.2% 24.12% and 41.02%

Explanation:

Step1: Recall the formula for coefficient of variation (CV)

The formula for the coefficient of variation is \( CV=\frac{\text{Standard Deviation (SD)}}{\text{Mean (}\bar{x}\text{)}}\times100\% \).

Step2: Calculate CV for the first section

For the first section, mean (\(\bar{x}_1\)) = 55 and standard deviation (\(SD_1\)) = 15.
Using the formula, \( CV_1=\frac{SD_1}{\bar{x}_1}\times100\%=\frac{15}{55}\times100\% \)
\(\frac{15}{55}\approx0.2727\), so \( CV_1\approx0.2727\times100\% = 27.27\% \)

Step3: Calculate CV for the second section

For the second section, mean (\(\bar{x}_2\)) = 30 and standard deviation (\(SD_2\)) = 10.
Using the formula, \( CV_2=\frac{SD_2}{\bar{x}_2}\times100\%=\frac{10}{30}\times100\% \)
\(\frac{10}{30}\approx0.3333\), so \( CV_2\approx0.3333\times100\% = 33.33\% \)

Answer:

B. 27.27% and 33.33%