Question

The marks obtained by 9 students in Mathematics are 59, 46, 30, 23, 27, 44, 52, 40 and 29. The median of the data is ??????????????

Answer 1

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Given set of numbers:

• 59, 46, 30, 23, 27, 44, 52, 40, 29

No of observations = 9

First we have to arrange the given set of numbers in ascending or descending order:

➝ 23, 27, 29, 30, 40, 44, 46, 52, 59

To find the median, you need to put the values in order, then find the middle value. If there are two values in the middle then you find the mean of these two values.

Since the no. of observations is odd, the middle value of the data will be the median. Middle term will be the 5th term i.e. 40

And we are done !!!

Answer 2

Answer :-

» The median of data = 40

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★ Concept :-

Here the concept of Median of Ungrouped Data is used. The given things and data are raw and Ungrouped. So their median value will be the middle most value.

• When the number of observations is odd :-

Take median as middle most term or value.

• When the number of observations is even :-

Take the mean or average of the two most middle terms.

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★ Solution :-

Here the given frequencies are :-

• 59, 46, 30, 23, 27, 44, 52, 40 and 29

Let us first arrange them in an specified order that is ascending or descending. Here we are going with ascending order.

✏ 23, 27, 29, 30, 40, 44, 46, 52, 59

• We see here there are 9 terms. So clearly, using the rule of odd terms, we will take the middle most value.

Here the middle most value is 5th term that is 40 .

✒ So the median of the given data is 40.

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★ More to know :-

• Mean of Ungrouped Data :- It is taken as the sum of all the observations divided by total number of observations.

• Mode of Ungrouped Data :- It is taken as the observation with highest number of frequency.

• Mean also known as arithmetic mean is the average value of all the observations.

• Mode is the the most occurring observation. If V is a discrete random variable, the mode is the value v at which the probability mass function takes its maximum value.

• Median is the middle most value of the given observations when arranged in ascending or descending order. If there is an odd amount of numbers, the median value is the number that is in the middle, with the same amount of numbers below and above.