Question

1. what is the iqr? number of branches on 10 year old trees a. 5 branches b. 7 branches c. 10 branches d. 12 branches (from unit 1, lesson 11.) unit 1 lesson 13 cumulative practice problems 10. three drivers competed in the same fifteen drag races. the mean and standard deviation for the race times of each of the drivers are given. driver a had a mean race time of 4.01 seconds and a standard deviation of 0.05 seconds. driver b had a mean race time of 3.96 seconds and a standard deviation of 0.12 seconds. driver c had a mean race time of 3.99 seconds and a standard deviation of 0.19 seconds. a. which driver had the fastest typical race time? b. which driver’s race times had the highest variability? c. which driver do you predict will win the next drag race? support your prediction using the mean and standard deviation.

Explanation:

Step1: Recall IQR definition

The inter - quartile range (IQR) is the difference between the third quartile ($Q_3$) and the first quartile ($Q_1$). In a box - and - whisker plot, the left - hand edge of the box is $Q_1$ and the right - hand edge of the box is $Q_3$.

Step2: Identify $Q_1$ and $Q_3$ from the box - and - whisker plot

From the box - and - whisker plot of the number of branches on 10 - year - old trees, $Q_1 = 8$ and $Q_3=13$.

Step3: Calculate the IQR

$IQR=Q_3 - Q_1=13 - 8 = 5$

Step1: Analyze mean for fastest typical time

The mean represents the typical value. The smaller the mean race time, the faster the typical race time. Driver B has a mean race time of 3.96 seconds, Driver A has a mean of 4.01 seconds and Driver C has a mean of 3.99 seconds. Since 3.96<3.99<4.01, Driver B has the fastest typical race time.

Step2: Analyze standard deviation for variability

The standard deviation measures the amount of variation or dispersion. The larger the standard deviation, the higher the variability. Driver A has a standard deviation of 0.05 seconds, Driver B has a standard deviation of 0.12 seconds and Driver C has a standard deviation of 0.19 seconds. Since 0.19>0.12>0.05, Driver C has the highest variability in race times.

Step3: Make a prediction for the next race

Driver B has the fastest mean race time, which indicates that on average, Driver B is the fastest. Also, Driver B's standard deviation (0.12 seconds) is not the highest. So, Driver B is a good prediction to win the next race as they have a fast average time and not too high variability.

Answer:

A. 5 branches