1. Box-and-whiskers Plot
Box-and-whiskers plot is a graphical representation of data that shows the values of quartiles (i.e. quartile 1, 2 and 3) within a rectangular box. In this graph, the ends of the box represent quartile 1 (Q1) and quartile 3 (Q3), while quartile 2 (Q2) represents the median-the horizontal line inside the box. The length of the box-the difference between Q1 and Q3-is known as the interquartile range (i.e. IQR = Q3-Q1). Whiskers are lines inside the box drawn at the median. These lines represent extreme values within the observable range. It is also the line which corresponds to a positive (+) sign at the mean. These lines extend up to 1.5 times the interquartile range from both ends of the box. The function of whiskers is to connect the values outside the range of the box that are not higher than 1.5 the interquartile range away from the box. The value within the given range falls under the category of observed values while values beyond the whiskers are called outliers (Larson 80; McCluskey and Lalkhen 128).
2. Standard Deviation
Standard deviation is a measure of variability. It shows the distribution or the spread of data. Mathematically, it is defined as the square root of variances. Unlike the variance, standard deviation has the same unit as the original observation. It is also a measure of the mean distance of individual values from the mean. When the mean value is lower than the standard deviation, it loses its power to measure central tendency. The rule of thumb is that smaller standard deviation indicates that individual values are closer to one another (i.e. precise), while large standard deviation implies a larger variation between individual values (Driscoll, Lecky and Crosby 277; Silluvan 449).
3. Normal Distribution
The normal distribution, also referred to as Gaussian distribution uses two parameters to define the shape of the distribution. These parameters include the mean and standard deviation. When the data is graphed using a histogram or a line graph, the normal distribution exhibits the following characteristics: unimodal, symmetrical and (McCluskey and Lalkhen 128)
The standard normal distribution has a mean value equal to zero and a standard deviation equal to one. It is also referred to as the z-distribution. The z-value under this distribution refers to the number of standard deviation (SD), where the value of a single datum is above or below the mean. The standard normal distribution is used to compare two different normal distributions (McCluskey and Lalkhen 129).
Works Cited
P. Driscoll, F. Lecky and M. Crosby. "An introduction to Everyday Statistics—2." Journal of Accident and Medicine, 17(2000): 274-281. Print.
Larson, M. "Descriptive Statistics and Graphical Displays." Circulation, 114 (2006): 76-81. doi: 10.1161/CIRCULATIONAHA.105.584474. Web.
McCluskey A. and G. Lalkhen. "Statistics II: Central Tendency and Spread of Data." Continuing Education in Anaesthesia, Critical Care and Pain, 7.4(2007): 127-130. Print.
Sullivan, L. M. "Estimation From Samples." Circulation, 114(2006): 445-449. doi:10.1161/CIRCULATIONAHA.105.600189. Web.
