4. Lucy and Dena are training for a bike race and recorded their mileage for a week. Find the measures of variation of each person's mileage. Which measures of variation show the girls' similarities in their training? the differences? Explain. Lucy Dena Monday Tuesday Wednesday 7 mi 3 mi 5 mi 6 mi 4 mi 6 mi Thursday Friday 8 mi 6 mi 8 mi 11 mi Saturday Sunday 10 mi 9 mi 9 mi 7 mi

Question

4. Lucy and Dena are training for a bike race and recorded their mileage for a week. Find the measures of variation of each person's mileage. Which measures of variation show the girls' similarities in their training? the differences? Explain. Lucy Dena Monday Tuesday Wednesday 7 mi 3 mi 5 mi 6 mi 4 mi 6 mi Thursday Friday 8 mi 6 mi 8 mi 11 mi Saturday Sunday 10 mi 9 mi 9 mi 7 mi​

soldevillaelizerjohn · Answer

Answer:   There are several measures of variation that you can use to compare the girls' mileage. One measure of variation is the range, which is the difference between the maximum and minimum values. For Lucy, the range of her mileage is 10-3=7 miles, and for Dena, the range is 11-4=7 miles. Another measure of variation is the interquartile range, which is the difference between the upper and lower quartiles of the data. To find the interquartile range, you first need to find the median, or middle value, of the data. For Lucy, the median is (6+7)/2=6.5 miles, and for Dena, the median is (6+8)/2=7 miles. The upper quartile is the value that is greater than or equal to 75% of the data, and the lower quartile is the value that is less than or equal to 25% of the data. For Lucy, the upper quartile is 8 miles and the lower quartile is 5 miles, so the interquartile range is 8-5=3 miles. For Dena, the upper quartile is 9 miles and the lower quartile is 4 miles, so the interquartile range is 9-4=5 miles.    The range and interquartile range both show the differences in the girls' mileage, as they measure the spread of the data. However, the range is more sensitive to outliers, or values that are much larger or smaller than the rest of the data, while the interquartile range is less sensitive to outliers.    To compare the girls' similarities in their training, you could use the mean, or average, mileage. The mean mileage for Lucy is (7+3+5+6+4+6+8+6+10+9)/10=6.1 miles, and the mean mileage for Dena is (6+4+6+8+11+9+7)/7=7.1 miles. The mean shows that the girls have similar levels of training, as they both average around 6-7 miles per day. You could also use the standard deviation, which measures the average amount that the data values differ from the mean. The standard deviation for Lucy is sqrt(((7-6.1)^2+(3-6.1)^2+(5-6.1)^2+(6-6.1)^2+(4-6.1)^2+(6-6.1)^2+(8-6.1)^2+(6-6.1)^2+(10-6.1)^2+(9-6.1)^2)/9)=1.9 miles, and the standard deviation for Dena is sqrt(((6-7.1)^2+(4-7.1)^2+(6-7.1)^2+(8-7.1)^2+(11-7.1)^2+(9-7.1)^2+(7-7.1)^2)/6)=2.2 miles. The standard deviation shows that the girls have similar levels of variation in their training, as they both have standard deviations around 2 miles.

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