mode

Hello students, Previously we have discussed about what is cartesian product and In today's session we are going to discuss about mode which comes under cbse books, Mathematics covers many topics, statistics is one of them. In mathematics statistics plays a very important role to summarize the data by the various types. Mean, median and mode are the three measures of central tendency. But here we have to discuss the mode.

Mode in an ungrouped data, the most occurring term gives the data and if some terms have frequencies more than 1, then the term having the largest frequency is the mode.

 In a grouped data we have

Mode = L1+ (f-f1) / (2f – f1 - f2) * (L2 - L1), where L is the lower limit of model class, f is the frequency of model class and f1 and f2 are the respective frequencies of the preceding and succeeding classes of the model class.

Let’s take some example of mode:

Example 1: What is the mode of 5, 7, 9, 12, 10, 15, 7, 8, 7, 25?

Solution: Since 7 occurs most often, so mode = 7

Example 2: Find the mode of the following frequency distribution

Term               25        35        45        55        65

Frequency      4          9          16        13        6

Solution: Since 45 occurs most often, so mode = 45

Example 3: Find the mode from the data given below

Marks obtained          0-5      5-10   10-15             15-20             20-25             25-30

            Number of students  18        20          25                    30                    16                    14

Solution: The maximum frequency is 30. So mode class is 15-20

 L1 =15 L2 =20, f = 30, f1 = 25 and f2 = 16.

Mode = L1+ (f-f1) / (2f – f1 - f2) * (L2 - L1) = = 15+ (30 - 25) / (60 – 25 - 16) * (20 - 15) = 16.3

So exact values is 16.3

In the next session we will discuss about range and You can visit our website for getting information about calculus tutor.

How to calculate Median

Median is a special kind of average which is used to calculate the average value of the given objects value. In statistics, median can be described as the numerical value which separates the any given sample values into two half. In the concept of statistical average, we generally studied about the three most popular concept that are mean, median and mode. All these are similar kind of average. Here we are going to discussing about the median. Median can be specifies as the middle value in the list of values. In the concept of median, when we perform the total of the list is odd, and then we select the middle entry in the list after sorting the list into the increasing order. Sometime the concept of mean is not performing very well when the sum of the given list is odd. If in case the total of the list are even, the median is equal to the sum of the two middle numbers divided by two. But the operation of median can only be performed by sorting the list into increasing order. There are some of the step that needs to be following while performing the median on the list values. (know more about cbse board papers, here)
These steps are considered as a formula for calculating the median.
(a)     First of all arrange the values in the increasing order.
(b)     After that select the middle value from the list. These values consider as a median of the list.
(c)     If in case the middle value contains two values then divides the sum of these two middle values by two.
Formula of median = L + H / 2
In above L refers to lowest middle value and H refers to larger middle value.
Now we show you the concept of median by performing the example in the below:
Example: Suppose there are five children who have the different amount in there pocket. These are 9, 3, 44, 17 and 15. Now we need to calculate the median of these values?
Solution: In above question given that amount of five children are 9, 3, 44, 17 and 15.
So, first we need to arrange them in increasing order that is:
               3, 9, 15, 17, 44
By following the above sequence of number the median is: 15
In the next session we will discuss about Probability and Statistics.