Median of grouped data is the data that is continuous and is in the form of frequency distribution. Median is the middlemost value of the given data that separates the higher half of the data from the lower half. While calculating the median of grouped data, the middle value is not known as the data is divided into class intervals. Let us learn more on how to calculate the median of grouped data, the median formula, and solve a few examples to understand this concept better. Show
What is Median of Grouped Data?Median of a grouped data is data that is arranged in ascending order and is written in a continuous manner. The data is in the form of a frequency distribution table that divides the higher level of data from the lower level of data. One of the simplest methods of finding the median of grouped data is by using the formula. As finding the middle value or median of a grouped data might be tough. Therefore, to find the median for grouped data we can use the following steps and formula:
Where,
Definition of MedianMedian is the middlemost value in a given data set after it is arranged in ascending order. If the total number of items in the list is odd, then after arranging the values in the ascending order the middlemost value is taken as the median i.e. the median is given by the [(n+1)/2]th term, where 'n' is the total number of observations. If the number of items in the data set is even, then the average of the two middle values is taken, that is, [(n/2)th term + ((n/2) + 1)th term] / 2, where 'n' is the total number of observations. For example: Let's consider the data: 48, 20, 50, 69, 73. What is the median? Solution: Arranging in ascending order, we get: 20, 48, 50, 69, 73. Here, n (no.of observations) = 5 So, to find the median of odd data we use the formula: [(n+1)/2] = (5 + 1)/2 = 6/2 = 3 Therefore, Median = 3rd observation Median = 50. Steps to Find Median of Grouped DataMedian of grouped data is in the form of a frequency distribution arranged in ascending order and is continuous. Find the median of any given data is simple since the median is the middlemost value of the data. Since the data is grouped, it is divided into class intervals. Let us learn the steps to finding the median of grouped data.
Let us look at an example to understand this better. For Example: Calculate the median for the following data:
Solution: We need to calculate the cumulative frequencies to find the median.
N = sum of cf = 80, N/2 = 80/2 = 40 Since n is even, we will find the average of the n/2th and the (n/2 +1)th observation i.e. the cumulative frequency greater than 40 is 63 and the class is 40 - 60. Hence, the median class is 40 - 60. l = 40, f = 37, c = 26, h = 20 \(\) Using Median formula: Median = l + [(n/2−c)/f] × h = 40 + [(37 - 26)/40] × 20 = 40 + (11/40) × 20 = 40 + (220/40) = 40 + 5.5 = 45.5 Therefore, the median is 45.5. Median of Grouped Data FormulaThe formula to calculate the median of grouped data is the same as mentioned above. The data needs to be continuous and in the form of a frequency distribution and the median is calculated through the following sequence of steps.
Hence the formula is, Median = l + [(n/2−c)/f] × h Related Topics:Listed below are a few interesting topics related to the median of grouped data, take a look.
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FAQs on Median of Grouped DataMedian of grouped data is the data formed in a frequency distribution table in ascending order with the values being continuous. Median is considered as the middle value of any data with values in an even or odd manner. For a grouped data, a frequency distribution is required to find the median and is done by using the formula. Median = l + [(n/2−c)/f] × h. What is the Formula for Median of Grouped Data?The formula for median of grouped data depends on the observations, the class size, the frequency, and the cumulative frequency. The formula to calculate the median is l + [(n/2−c)/f] × h. Where,
What are the Steps to Find Median of Grouped Data?The steps to find the median of grouped data is as follows:
What is Meant By Median in Statistics?The value of the middle-most observation obtained after arranging the data in ascending or descending order is called the median of the data. When describing a set of data, the central position of the data set is identified and used further in the median formula. This is known as the central measure of tendency. Median is an important measure of central tendency. Why Median is Called Positional Average?The median falls in the middle when the data is arranged in an increasing or decreasing order. Hence the median is referred to as positional average. The median is the exact middle value, in case of odd number of data points whereas for even number of data points, the median is the average of the two middle values. |