Question

the table shows the total number of student applications to universities in a particular state for a random sample of 12 semesters

what is the approximate sample mean for student applications, in thousands?

a 2,565
b 214
c 329

Explanation:

Step1: Calculate the sum of all values

$$106 + 137+285 + 120+202+195+327+139+307+318+212+217$$
$$=(106 + 137)+(285 + 120)+(202 + 195)+(327 + 139)+(307 + 318)+(212 + 217)$$
$$=243+405+397+466+625+429$$
$$=(243 + 405)+(397 + 466)+(625 + 429)$$
$$=648+863+1054$$
$$=2565$$

Step2: Calculate the sample mean

The formula for the sample mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $n = 12$ (the number of semesters) and $\sum_{i=1}^{n}x_{i}=2565$
$$\bar{x}=\frac{2565}{12}=213.75\approx214$$

Answer:

B. 214