Help pls ? What is variance and standard deviation for the following simple frequency distribution collected

Question

What is variance and standard deviation for the following simple frequency distribution collected from 18 college students as to the number of their friends, from 1 to 5, calculate the mean; mean squared, variance and standard deviation. Show steps?

https://s.yimg.com/tr/i/8a88e13ef19e43318192af18fd986007_A.jpeg

https://docs.google.com/document/d/15PGdLxXqkg7as6bDc0sJQjH38kSqOAt9uAhMIp40nio/edit?usp=sharing

Answer 1

The mean is the sum of values multiplied by the frequency divided by the sum of observations, i.e.:

mean = (1*(2) + 2*(2) + 3*(6) + 4*(5) + 5*(3)) / 18 = 3.277778

mean squared is simple (although I don't know why you're being asked for it): (3.277778)^2 = 10.74383

Variance is the sum of (value (1 to 5) * frequency - mean)^2 / 18 = 1.506536

Standard deviation is the square root of variance: 1.22741

Note that these are biased estimates. If you want unbiased estimates (which I'm guessing is not the case here), you would multiple variance by (18/17), and multiple standard deviation by the square root of (18/17).