normal distribution curve

right skewed distributions

- majority of data values fall to the left of the mean so the distribution called positive or right skewed - the mean is to the right of the median and the mean and the median are to the right of the mode mean >median > mode

left skewed distribution

- majority of data values fall to the right of the mean so the distribution called negative or left skewed - the mean is to the left of the median and the mean and median to the left of the mode mean < median <mode

skewed distribution

- normal distribution is continuous bell shaped distribution of variable - if data values are distributed about the mean the distribution is called symmetrical - if the majority of data values fall to the left or to the right of the mean the distribution is called skewed

the shape and position of the normal distribution curve depends on two parameters

1- mean 2- standard deviation

characteristics of normal distribution

1- normal distribution curve is bell shape 2- mean , median , and mode are equal and located at the center of the distribution 3- normal distribution curve is unimodal (single mode ) 4- the curve is symmetrical about the mean 50% of the values lie above the mean (to the right ) and 50% of the values lie below the mean (to the left ) 5 -the curve is continuous 6- the curve never touches the X axis 7- the total area under the normal curve that lies within - one standard deviation of the mean is approximately 68% - two standard deviations of the mean is approximately 95% - three standard deviations of the mean is approximately 99.7%

advantages of normal distribution

1- we can theoretically calculate how many observations will lie within given distance of the mean (not in term of actual unit ) - 95% of observations lie between mean and two standard deviation in which considered normal range or normal status - 5% of observations outside the normal range 2- determine the normal range of biological and medical variables whose distribution is known

Z- score

location of any observation can be expressed in terms of how many standard deviations lies above or below the mean of the distribution - above the mean = negative - below the mean = positive

distribution of many continuous variables is pell shaped called

normally distributed variables or bell curve or Gaussian distribution

spread of normal distribution is controlled by

standard deviation