**Normal Distribution:**

The normal distribution, also known as the Gaussian distribution or bell curve, is a symmetrical probability distribution that is characterized by a bell-shaped curve.

Get the **full solved assignment PDF of MPC-006 of 2023-24** session now.

In a normal distribution:

- The mean (average), median, and mode are all equal and located at the center of the distribution.
- The distribution is symmetric, meaning the left and right sides of the mean are mirror images of each other.
- About 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.

The normal distribution is a theoretical concept used in statistics, and many natural phenomena tend to follow this distribution, such as the distribution of heights, weights, IQ scores, and measurement errors.

**Divergence from Normality:**

Divergence from normality refers to situations where the data does not conform to the characteristics of a normal distribution. There are several ways in which data may diverge from normality:

**Skewness:**A normal distribution is symmetric, but if the data is skewed, it means that the distribution is not symmetrical. Positive skewness indicates a longer right tail, while negative skewness indicates a longer left tail.**Kurtosis:**Kurtosis measures the “tailedness” of a distribution. A normal distribution has a kurtosis of 3 (mesokurtic). Higher kurtosis (leptokurtic) indicates heavier tails, and lower kurtosis (platykurtic) indicates lighter tails.**Outliers:**Extreme values, or outliers, can significantly affect the normality of a distribution. Outliers may cause skewness or kurtosis, impacting the symmetry and tail behavior.**Multimodality:**A normal distribution is unimodal (has one peak). If a distribution has more than one peak, it is multimodal and diverges from normality.**Heavy Tails:**Tails that are heavier than those of a normal distribution can affect the overall shape. This is often observed in distributions with extreme values or in fat-tailed distributions.**Non-Linearity:**In some cases, the relationship between variables may be non-linear, leading to a departure from normality.

When data diverges from normality, it may impact the validity of statistical analyses that assume normal distribution, such as parametric tests like t-tests or analysis of variance (ANOVA). In such cases, non-parametric tests or data transformation techniques may be considered. It’s important for researchers to assess the normality of their data before applying statistical methods that assume a normal distribution and, if necessary, explore alternative approaches that are robust to deviations from normality.