First we arrange them in a column headed x.  Add the column,
and divide by the number of values, which is 10

     x
    17
    18
    19
    21
    22
    22
    23
    24
    28
    29
  ______
10)223.0
    22.3
   _
So x = 22.3 = the mean. 

To find the median, we average the two numbers in the middle when
they are arranged from smallest to largest.  The two numbers in
the middle are 22 and 22, and their average is 22, so the median
is 22.

The number occurring the most number of times is the mode.  22
occurs twice in the column, so the mode is 22.

To find the sample variance, out beside that column we write
a second column headed 
  _
x-x and the numbers in that bar are the numbers in the x column with
the mean 22.3 subtracted from them

            _ 
     x    x-x
    17   -5.3
    18   -4.3
    19   -3.3
    21   -1.3
    22   -0.3
    22   -0.3
    23    0.7
    24    1.7
    28    5.7
    29    6.7
  ______
10)223.0
    22.3

Out beside that column we make a thrid column of squaring the number
in the column and we head it:
   _
(x-x)²

We add that column and divide by 1 less than the number of
values, which means we divide by 10-1 or 9:
            _ 
     x    x-x   (x-x)²
    17   -5.3   28.09
    18   -4.3   18.49
    19   -3.3   10.89
    21   -1.3    1.69
    22   -0.3    0.09
    22   -0.3    0.09
    23    0.7    0.49
    24    1.7    2.89
    28    5.7   32.49 
    29    6.7   44.89
  ______      _______
10)223.0     9)140.10
    22.3        15.56666... round to 15.57

The variance is 15.57

It is not normally distributed because there is only
1 of each data value except 22.  If you draw a histogram 
of the data it is not mound-shaped at all.

Edwin