[Script Info]
Title:
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.00,0:00:05.00,Default,,0000,0000,0000,,And obviously the new mean is 1.2 times the old mean because we're multiplying
Dialogue: 0,0:00:05.00,0:00:11.00,Default,,0000,0000,0000,,everything up by 20% raise that makes a factor of 1.2 over here and zero over here
Dialogue: 0,0:00:11.00,0:00:15.00,Default,,0000,0000,0000,,because we don't really add a constant amount of money per person its variable.
Dialogue: 0,0:00:15.00,0:00:19.00,Default,,0000,0000,0000,,It's a multiplicative change. For the variance it's more interesting.
Dialogue: 0,0:00:19.00,0:00:27.00,Default,,0000,0000,0000,,In our new variance, we multiply each salary by a factor of 1.2 and the same is through for the mean.
Dialogue: 0,0:00:27.00,0:00:34.00,Default,,0000,0000,0000,,When we look at this, we can bring the 1.2 outside these brackets and it becomes (1.2)².
Dialogue: 0,0:00:34.00,0:00:40.00,Default,,0000,0000,0000,,The reason why I squared this, we can bring it outside Xi and u but there's a square over here
Dialogue: 0,0:00:40.00,0:00:42.00,Default,,0000,0000,0000,,and we can move it outside this sum as a factor.
Dialogue: 0,0:00:42.00,0:00:45.00,Default,,0000,0000,0000,,Now this is true for the variance but not the standard deviation.
Dialogue: 0,0:00:45.00,0:00:48.00,Default,,0000,0000,0000,,The standard deviation is cleared of the variance.
Dialogue: 0,0:00:48.00,0:00:55.82,Default,,0000,0000,0000,,The standard deviation was up by factor of 1.2 only, with a constant offset of zero.