What is the standard deviation of the distribution?

Question

This equation comes from Edgenuity's course of Statistics, and I am taking the course as a high school senior. I understand how to find the standard deviation.

Standardized tests for certain subjects, given to high school students, are scored on a scale of 1 to 5. Let X represent the score on a randomly selected exam. The distribution of scores for one subject’s standardized test is given in the table.

What is the standard deviation of the distribution?

A. 1.3

B. 1.6

C. 1.7

D. 2.5

Firstly, I used the standard deviation equation using the mean of the probabilities and using each probability value and its distance from the mean. Since my final calculation 0.041 is not one of the answer choices, I noticed in my deeper analysis that these values are the probabilities, not the distribution of scores. So, I multiplied the score number (i.e., 1, 2, 3, etc.) by each probability value each score is assigned to. I found the values to be 0.18, 0.4, 0.78, 0.84, 0.75. I entered the mean and their distance from it in the standard deviation equation, and found the answer to be 0.2865, which is not one of the answer choices. 

Unless there is an error in the answer choices, what steps do I need to do to find the correct answer? What methods am I doing incorrectly?

Answer 1

Go back to the raw data. Assume you have 100 people then

the frequencies are 18, 20, 26, 21 and 15.

So on a TI 84 you can make 2 lists.

L1 - 1,2,3,4,5

L2 - 18,20, 26, 21, 15

Then stat calc

1 var stats

list = l1

freqlist = l2

calculate

standard deviation = 1.3143