Question

a stock broker compiled data about 50 popular stocks. he made this frequency table to show how their changes in 2010 compared to their changes in 2009. complete a relative frequency table to show the distribution of the data with respect to all 50 stocks. complete the table. total relative frequency table change in 2009 changes in 2010 positive change negative change total positive change % % % negative change % % % total % % % (for integers or decimals) frequency table change in 2009 changes in 2010 positive change negative change total positive change 11 10 21 negative change 14 15 29 total 25 25 50

Explanation:

Step1: Understand Relative Frequency

Relative frequency is calculated as $\frac{\text{Frequency of a category}}{\text{Total number of observations}} \times 100\%$. Here, the total number of stocks is 50.

Step2: Calculate for "Positive Change" in 2010 - Positive Change in 2009

Frequency is 11. Relative frequency: $\frac{11}{50} \times 100\% = 22\%$

Step3: Calculate for "Positive Change" in 2010 - Negative Change in 2009

Frequency is 10. Relative frequency: $\frac{10}{50} \times 100\% = 20\%$

Step4: Calculate for "Positive Change" in 2010 - Total

Total frequency for "Positive Change" in 2010 is $11 + 10 = 21$. Relative frequency: $\frac{21}{50} \times 100\% = 42\%$

Step5: Calculate for "Negative Change" in 2010 - Positive Change in 2009

Frequency is 14. Relative frequency: $\frac{14}{50} \times 100\% = 28\%$

Step6: Calculate for "Negative Change" in 2010 - Negative Change in 2009

Frequency is 15. Relative frequency: $\frac{15}{50} \times 100\% = 30\%$

Step7: Calculate for "Negative Change" in 2010 - Total

Total frequency for "Negative Change" in 2010 is $14 + 15 = 29$. Relative frequency: $\frac{29}{50} \times 100\% = 58\%$

Step8: Calculate for "Total" - Positive Change in 2009

Total frequency is $11 + 14 = 25$. Relative frequency: $\frac{25}{50} \times 100\% = 50\%$

Step9: Calculate for "Total" - Negative Change in 2009

Total frequency is $10 + 15 = 25$. Relative frequency: $\frac{25}{50} \times 100\% = 50\%$

Step10: Calculate for "Total" - Total

Total frequency is 50. Relative frequency: $\frac{50}{50} \times 100\% = 100\%$

Answer:

Change in 2010 \ Change in 2009	Positive Change	Negative Change	Total
Negative Change	20%	30%	50%
Total	42%	58%	100%