Question

1. calculate the mean number of minutes it takes andre to hike a mountain. 2. what do you think will happen to the mean time for the week if andre decides to take pictures of the rocks, wildflowers, and wildlife throughout the hike for the seventh day? 3. calculate the mean number of minutes including the time it took andre on the seventh day (50, 52, 55, 59, 50, 130). 4. 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, 55, 59, 50, 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 first part (no seventh - day data)

Since no data for the first six - day is given, we'll assume we are working with the data for the case with the seventh - day data. Let the data set be $x=\{50,52,55,59,50,130\}$. Here $n = 6$.
$\sum_{i=1}^{6}x_{i}=50 + 52+55+59+50+130=396$.
The mean $\bar{x}_1=\frac{396}{6}=66$.

Step3: Analyze effect of taking pictures on seventh day

If Andre takes pictures on the seventh day and the time is $130$ minutes (a relatively large value compared to the other values), it will increase the sum of the data values. Since the number of data - points $n$ also increases by $1$ (from $6$ to $7$), but the large value of $130$ has a significant impact on the sum, the mean will increase.

Step4: Calculate mean with seventh - day data

Let the data set be $x=\{50,52,55,59,50,130,50\}$. Here $n = 7$.
$\sum_{i = 1}^{7}x_{i}=50+52+55+59+50+130+50 = 446$.
The mean $\bar{x}_2=\frac{446}{7}\approx63.71$.

Step5: Calculate mean with Andre's estimate for seventh day

Let the data set be $x=\{50,52,55,59,50,60,50\}$. Here $n = 7$.
$\sum_{i=1}^{7}x_{i}=50 + 52+55+59+50+60+50=376$.
The mean $\bar{x}_3=\frac{376}{7}\approx53.71$.

Answer:

1. Mean without seventh - day data (assuming we start with six - day data not given, but using first six values of given sets): 66
2. Effect of taking pictures on seventh day: The mean will increase.
3. Mean with seventh - day data ($130$ minutes on seventh day): $\approx63.71$
4. Mean with Andre's estimate for seventh day ($60$ minutes on seventh day): $\approx53.71$