This post deals only with quantitative data.
When you have a quantitative dataset, it is always a good idea to look at a graphical display of it: usually a histogram or boxplot, although there are others. What you are looking to describe is the shape of the data (the subject of a recent post), the approximate center of the dataset, the spread of the values, and any unusual features (such as extremely low or high values -- outliers). We'll take them one at a time.
Shape
The shape of the dataset helps us determine how to report on the other features. We went into detail about shape in a very recent post ("The Shape of a Quantitative Distribution"). If the display is basically symmetric, you will use the mean to describe the center and a measure called the Standard deviation to describe the spread. If the display is non-symmetric, you will use the median to describe the center and the interquartile range to describe the spread. Here's a handy chart to summarize this.
Center
In a symmetric distribution the mean and median are at approximately the same place; however, statisticians use the mean. In a non-symmetric distribution, the median is used because by its very definition, it is not calculated using any extreme points or points that skew the calculation.
Spread
Notice that the range (which is the difference between the largest and smallest data value in the set) is not generally used to describe the spread. In a symmetric distribution we use the standard deviation, which has a complicated formula but a simple description: the Standard Deviation is the average squared difference between each value in the dataset and the mean of the dataset. You can find the standard deviation using a graphing calculator or a tool like MS-Excel. The symbol for Standard Deviation is
Standard deviations are relative. By that I mean that you can't tell just by looking at its value whether it's large or small -- it depends on the values in the dataset. Standard deviations are good for comparing spreads if you have two distributions. And, we'll soon find out that the standard deviation has an extremely important use in statistics. Here's an example for finding the mean and standard deviation using MS-Excel:
In a non-symmetric distribution we use the Interquartile Range (IQR) because this tells the spread of the central 50% of the data values. Like the median, the IQR isn't influenced by outliers or skewness. Here's an example of finding the median and IQR using MS-Excel:
Unusual Features
As mentioned above, unusual features include extreme points (if any), also known as outliers. In an earlier post, we covered how to determine the boundaries for outliers. If a data value lies outside the boundaries, we call it an outlier. If a value isn't quite an outlier but close, it's worth mentioning in a description of a distribution. Just call it an "extreme point."
There is a safe & effective Natural Herbal Medicine. For Total Cure Call +2349010754824, or email him drrealakhigbe@gmail.com For an Appointment with (Dr.) AKHIGBE contact him. Treatment with Natural Herbal Cure. For:Dengue Fever, Malaria. Painful or Irregular Menstruation. HIV/Aids. Diabetics. Vaginal Infections. Vaginal Discharge. Itching Of the Private Part. Breast Infection. Discharge from Breast. Breast Pain & Itching. Lower Abdominal Pain. No Periods or Periods Suddenly Stop. Women Sexual Problems. High Blood Pressure Chronic Disease. Pain during Sex inside the Pelvis. Pain during Urination. Pelvic Inflammatory Disease, (PID). Dripping Of Sperm from the Vagina As Well As for Low sperm count. Parkinson disease. Obesity, Lupus. Cancer. Tuberculosis. Zero sperm count. Bacteria, Impotence Fertility,Protoplasmic, Diarrhea. Herpatitis A&B, Rabies. Asthma. Quick Ejaculation. Gallstone, Cystic Fibrosis, Schizophrenia, Cirrhosis, Premature Ejaculation. Herpes. Joint Pain. Stroke. Cornelia Disease, Weak Erection. Ovarian problem, Erysipelas, Thyroid, Discharge from Penis. Bronchial Problem, HPV. Hepatitis A and B. STD. Staphylococcus + Gonorrhea + Syphilis. Heart Disease. Pile-Hemorrhoid.rheumatism, Impotence, thyroid, Autism, Sepsis Bacteria, Penis enlargement, Prostate Problem, Waist & Back Pain. Male Infertility and Female Infertility. Etc. Take Action Now. contact him & Order for your Natural Herbal Medicine: +2349010754824 and email him drrealakhigbe@gmail.com Note For an Appointment with (Dr.) AKHIGBE.I suffered in Cancer for a year and three months dieing in pain and full of heart break. One day I was searching through the internet and I came across a testimony herpes cure by doctor Akhigbe. So I contact him to try my luck, we talk and he send me the medicine through courier service and with instructions on how to be drinking it.To my greatest surprise drinking the herbal medicine within three weeks I got the changes and I was cure totally. I don't really know how it happen but there is power in Dr Akhigbe herbal medicine. He is a good herbalist doctor.
ReplyDelete