statistic

 

Statistic

March , 2025

Basics of Statistics

By Deepanjali Sahoo  and Shewata Vikrant Patil

 

Definition: Science of collection, presentation, analysis, and reasonable interpretation of data.

 

Statistics presents a rigorous scientific method for gaining insight into data. For example, suppose we measure the weight of 100 patients in a study. With so many measurements, simply looking at the data fails to provide an informative account. However statistics can give an instant overall picture of data based on graphical presentation or numerical summarization irrespective to the number of data points. Besides data summarization, another important task of statistics is to make inference and predict relations of variables.

 

Statistical Description of Data

Statistics describes a numeric set of data by its    

• Center
• Variability
• Shape

Statistics describes a categorical set of data by    

• Frequency
• percentage or proportion of each category

 

Measures of central tendency

Whenever you measure things of the same kind, a fairly large number of such measurements will tend to cluster around the middle value. Such a value is called a measure of "Central Tendency". The other terms that are used synonymously are "Measures of Location", or "Statistical Averages". The most widely used measures of central tendency are Arithmetic Mean, Median, and Mode

Mean: Summing up all the observation and dividing by number of observations. 

 

Example- Mean of 20, 30, 40 is (20+30+40)/3 = 30. 

 

Median: The middle value in an ordered sequence of observations. That is, to find the median we need to order the data set and then find the middle value. In case of an even number of observations the average of the two middle most values is the median.

 

 Example - To find the median of {9, 3, 6, 7, 5}, we first sort the data giving {3, 5, 6, 7, 9}, then choose the middle value 6. If the number of observations is even, e.g., {9, 3, 6, 7, 5, 2}, then the median is the average of the two middle values from the sorted sequence, in this case, (5 + 6) / 2 = 5.5.

 

Mode: The value that is observed most frequently. The mode is undefined for sequences in which no observation is repeated.

 

Example - The life in number of hours of 10 flashlight batteries are as follows: Find the mode.

 

340 350 340 340 320 340 330 330 340 350

 

340 occurs five times. Hence, mode=340.

Mean or Median

The median is less sensitive to outliers (extreme scores) than the mean and thus a better measure than the mean for highly skewed distributions, e.g. family income. For example mean of 20, 30, 40, and 990 is (20+30+40+990)/4 =270. The median of these four observations is (30+40)/2 =35. Here 3 observations out of 4 lie between 20-40.  So, the mean 270 really fails to give a realistic picture of the major part of the data. It is influenced by extreme value 990