Distributions

Question 1

What is a negative skew

Answer 1

a negatively skewed distribution is one in which the tail of the distribution extends toward the lower values

Question 2

What are the 5 defining features of normal distribution

Answer 2

1. Symmetry and Bell-Shaped Curve
   The hallmark of normal distribution is its symmetric, bell-shaped curve. When graphed, the curve is centred around the mean, forming a shape that resembles a bell. The symmetry implies that the distribution is equally likely to produce values above or below the mean. This characteristic is essential for making predictions and understanding the distribution of data.
2. Central Tendency: Mean, Median, and Mode
   Normal distribution is centred around its mean (μ), median, and mode, and all three measures are equal in a perfectly normal distribution. The mean represents the average value, while the median and mode signify the centre of the distribution. This central tendency is crucial for understanding the typical or expected value in a set of data.
3. 68-95-99.7 Rule (Empirical Rule)
   A key feature of normal distribution is the 68-95-99.7 rule, also known as the empirical rule. This rule states that approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations. This provides a quick way to assess the spread of data and identify outliers.
4. Standard Deviation and Variance
   Normal distribution is characterized by a specific relationship between the mean and standard deviation. The standard deviation (σ) measures the extent to which data deviates from the mean. In a normal distribution, about 68% of data falls within one standard deviation, 95% within two, and 99.7% within three. This relationship allows for precise quantification of data dispersion.
5. Z-Score and Standardized Values
   The Z-score is a crucial characteristic associated with normal distribution. It represents the number of standard deviations a data point is from the mean. This standardized value allows for comparisons between different normal distributions, making it a valuable tool in statistical analysis.

Question 3

What is a positive skew

Answer 3

A positive value for skewness indicates that the tail is on the right side of the distribution, which extends towards more positive values

Question 4

What is skewed deviation

Answer 4

A skewed distribution occurs when one tail is longer than the other. Skewness defines the asymmetry of a distribution. Unlike the familiar normal distribution with its bell-shaped curve, these distributions are asymmetric.