We need to know how many students wrote more than 6 and fewer than 20 letters. Then, we count the number of x from 7 to 19:
7: 3
8: 2
9: 4
10: 0
11: 1
12: 0
13: 3
14: 2
15: 4
16: 0
17: 1
18: 2
19: 4
Then, adding these values:
![\#\text{ of x }=3+2+4+1+3+2+4+1+2+4=26](https://img.qammunity.org/2023/formulas/mathematics/college/z6ux8vkqrrwm2lt9y5yzv34jcsmti7fzqi.png)
Since each x represents two students, the corresponding number of students is:
![\begin{gathered} \#\text{ of students }=\#\text{ of x }\cdot2=26\cdot2 \\ \Rightarrow\#\text{ of students }=52 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/2pzpzm1zlrmu9jvu841wlsfomnu0cwnzkr.png)