Characteristics of a Normal distribution

• The normal distribution has two parameters viz. means ( µ) and standard deviation (σ).
• The normal curve is bell-shaped and symmetrical about the line z = µ.
• It has only one mode occurring at µ i.e. it is unimodal.
• The value of mean, median, mode will coincide at the center ( µ= x) because the distribution is symmetrical and single peaked.

i.e. Mean = Median = Mode = µ

• The normal curve has asymptotic tails i.e. progressively nearing the abscissa or x-axis.
• The range is unlimited, infinite in both directions but as the distance from µ increases, the curve approaches the horizontal axis more and more closely and never touches the horizontal axis ( x).
• It has two point of inflections, the points where the change in curvature occurs at a distance σ on either side of mean. The point of inflection of the normal curve at x= µ ± σ. The curve changes from concave to convex and vice-versa.
• The quartiles i.e Q₁ and Q₃ are equidistant from µ. i.e. Q₃– µ = µ – Q₁.
• The normal distribution is bilaterally symmetrical. So, it is free from skewness, its coefficient of skewness amounts to zero. i.e. Skewness = 0 and Kurtosis = 0.
• The range µ ± σ includes about 68% of the observations. The range µ ± 2σ includes about 95.46% of the observations. The range µ ± 3σ includes about 99.74% of the observations.