How to calculate Means, median and mode
IMPORTANT FORMULAS & CONCEPTS
How to calculate Means, median and mode: In many real-life situations, it is helpful to describe data by a single number that is most representative of the entire collection of numbers. Such a number is called a measure of central tendency. The most commonly used measures are as follows.
1. The mean, or average, of ‘ n ‘ numbers is the sum of the numbers divided by n.
2. The median of ‘ n ‘ numbers is the middle number when the numbers are written in order. If n is even, the median is the average of the two middle numbers.
3. The mode of ‘ n ‘ numbers is the number that occurs most frequently. If two numbers tie for most frequent occurrence, the collection has two modes and is called bimodal.
MEAN OF GROUPED DATA Direct method Mean, $$\bar{x}=\frac{\sum f_i x_i}{\sum f_i}$$ Assume mean method or Short-cut method Mean, $$\bar{x}=A+\frac{\sum f_i d_i}{\sum f_i}$$ where $$d_i=x_i-A$$ Step Deviation method Mean, $$\bar{x}=A+\frac{\sum f_i u_i}{\sum f_i} \times h$$ where $$u=\frac{x_i-A}{h}$$ MODE OF GROUPED DATA Mode $$=l+\left(\frac{f_1-f_0}{2 f_1-f_0-f_2}\right) \times h$$ where $$l=$$ lower limit of the modal class, $$h=$$ size of the class interval (assuming all class sizes to be equal), $$f_1=$$ frequency of the modal class, $$f_0=$$ frequency of the class preceding the modal class, $$f_2=$$ frequency of the class succeeding the modal class. Cumulative Frequency: The cumulative frequency of a class is the frequency obtained by adding the frequencies of all the classes preceeding the given class. MEDIAN OF GROUPED DATA Median $$=l+\left(\frac{\frac{n}{2}-c f}{f}\right) \times h$$ where $$l=$$ lower limit of median class, $$n=$$ number of observations, cf = cumulative frequency of class preceding the median class, $$f=$$ frequency of median class, $$h=$$ class size (assuming class size to be equal).
