Question

a. use technology to calculate the mean number of minutes it takes andre to hike a mountain. 52, 58, 55, 59, 50
b. what do you think will happen to the mean time for the week if andre decides to take pictures of the trees, waterfalls, and wildlife throughout the hike for the seventh day?
c. calculate the mean number of minutes including the time it took andre on the seventh day (130) 52, 58, 55, 59, 50, 130
d. if andre didnt stop to take pictures on the seventh day, he thinks he could have finished the trail in 60 minutes. calculate the mean hiking - time using andres estimate for the seventh day 50, 52, 58, 55, 59, 60

Explanation:

Step1: Recall mean formula

The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $x_{i}$ are the data - points and $n$ is the number of data - points.

Step2: Calculate mean for part a

The data set is $\{52,58,55,59,50\}$. Here $n = 5$, and $\sum_{i=1}^{5}x_{i}=52 + 58+55+59+50=274$. Then $\bar{x}=\frac{274}{5}=54.8$.

Step3: Analyze part b

If Andre takes pictures on the seventh day, the time on the seventh day is likely to be larger than the previous days' times. Since the mean is the sum of all values divided by the number of values, adding a larger value will increase the sum and thus increase the mean.

Step4: Calculate mean for part c

The data set is $\{52,58,55,59,50,130\}$. Here $n = 6$, and $\sum_{i = 1}^{6}x_{i}=52+58+55+59+50+130 = 404$. Then $\bar{x}=\frac{404}{6}\approx67.33$.

Step5: Calculate mean for part d

The data set is $\{52,58,55,59,50,60\}$. Here $n = 6$, and $\sum_{i=1}^{6}x_{i}=52 + 58+55+59+50+60=334$. Then $\bar{x}=\frac{334}{6}\approx55.67$.

Answer:

a. $54.8$
b. The mean will increase.
c. Approximately $67.33$
d. Approximately $55.67$