Here you will learn what is the formula for median of grouped and ungrouped data and how to find median with examples.<\/p>\n
Let’s begin –<\/p>\n
Median is defined as the measure of central term when they are arranged in ascending or descending order of magnitude.<\/p>\n
(i) For ungrouped distribution :\u00a0<\/strong>Let n be the number of variate in a series then<\/p>\n Median = \\(({n + 1\\over 2})^{th}\\) term, (when n is odd)<\/p>\n Median = Mean of \\(({n\\over 2})^{th}\\) and \\(({n\\over 2} + 1)^{th}\\) terms, (where n is even)<\/p><\/blockquote>\n Example<\/strong><\/span> : Find the median of 6, 8, 9, 10, 11, 12 and 13.<\/p>\n Solution<\/span><\/strong> : Total number of terms = 7<\/p>\n Here, n is odd.<\/p>\n The middle term = \\(1\\over 2\\)(7 + 1) = 4th<\/p>\n Median = Value of the 4th term =10<\/p>\n Hence, the median of the given series is 10.<\/p>\n (ii) For ungrouped frequency distribution :\u00a0<\/strong>First we prepare the cumulative frequency(c.f.) column and Find value of N then<\/p>\n Median = \\(({N + 1\\over 2})^{th}\\) term, (when N is odd)<\/p>\n Median = Mean of \\(({N\\over 2})^{th}\\) and \\(({N\\over 2} + 1)^{th}\\) terms, (where n is even)<\/p><\/blockquote>\n (iii) For grouped frequency distribution :\u00a0<\/strong>Prepare c.f. column and find value of \\(N\\over 2\\) then find the class which contain value of c.f. is equal or just greater to N\/2, this is median class<\/p>\n Median = \\(l\\) + \\(({N\\over 2} – F)\\over f\\)\\(\\times\\)h<\/p>\n where\u00a0 \\(l\\) – lower limit of median class<\/p>\n f – frequency of median class<\/p>\n F – c.f. of the class preceding median class<\/p>\n h – class interval of median class<\/p><\/blockquote>\n