Question

a park ranger wants to know the mean number of nights students in your school plan to camp next summer. the park ranger randomly surveys 10 students from each class. the results are shown.
nights camping
a: 0, 5, 2, 3, 0, 6, 0, 10, 3, 0
b: 14, 0, 0, 6, 5, 0, 1, 2, 2, 5
c: 8, 8, 2, 3, 4, 1, 0, 0, 0, 6
d: 10, 10, 5, 6, 1, 0, 0, 0, 4, 0
a. use each sample to make an estimate for the mean number of nights students in your school plan to camp next summer.
sample a b c d
mean □ □ □ □

Explanation:

Step1: Calculate the mean for sample A

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. For sample A: $x=\{0,5,2,3,0,6,0,10,3,0\}$, $n = 10$.
$\sum_{i=1}^{10}x_{i}=0 + 5+2+3+0+6+0+10+3+0=29$
$\bar{x}_A=\frac{29}{10}=2.9$

Step2: Calculate the mean for sample B

For sample B: $x=\{14,0,0,6,5,0,1,2,2,5\}$, $n = 10$
$\sum_{i=1}^{10}x_{i}=14 + 0+0+6+5+0+1+2+2+5=35$
$\bar{x}_B=\frac{35}{10}=3.5$

Step3: Calculate the mean for sample C

For sample C: $x=\{8,8,2,3,4,1,0,0,0,6\}$, $n = 10$
$\sum_{i=1}^{10}x_{i}=8 + 8+2+3+4+1+0+0+0+6=32$
$\bar{x}_C=\frac{32}{10}=3.2$

Step4: Calculate the mean for sample D

For sample D: $x=\{10,10,5,6,1,0,0,0,4,0\}$, $n = 10$
$\sum_{i=1}^{10}x_{i}=10+10 + 5+6+1+0+0+0+4+0=36$
$\bar{x}_D=\frac{36}{10}=3.6$

Answer:

Sample A: $2.9$, Sample B: $3.5$, Sample C: $3.2$, Sample D: $3.6$