Here we can use the formula

$$\begin{gathered} \text{Average (A)=}\frac{\mathrm{Sum} \mathrm{of} \mathrm{observations} \left(\mathrm{S}\right)}{\mathrm{No}. \mathrm{of} \mathrm{observations} \left(\mathrm{N}\right)} \\ \text{⇒ S=A×N} \end{gathered}$$

According to the question,

Sum of height of 27 persons (A=162, N=27)

⇒S=162 X 27 =4374

Later, Shreya's height was deleted, the average height reduced by 1 cm. (so A=161, N=26)

So, sum of height of 26 persons

⇒S=161 X 26 =4186

Now,

Shreya's height =(sum of height of 27 persons)-(Sum of height of 26 persons)

=4374-4186

=188 cm.

Hence, Option E is correct.