a collection of 20 distinct numbers have 13 as their median .A number is added to this collection but the median does not change what .what number is added
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Answer:
Mean, median, and mode are three kinds of “averages”. There are many “averages” in statistics, but these are, the three most common, and are certainly the three you are most likely to encounter in your CAT exams, if the topic comes up at all.
The “mean” is the “average” you’re used to, where you add up all the numbers and then divide by the number of numbers.
The “median” is the “middle” value in the list of numbers. To find the median, your numbers have to be listed in numerical order from smallest to largest, so you may have to rewrite your list before you can find the median.
The “mode” is the value that occurs most often. If no number in the list is repeated, then there is no mode for the list.
The “range” of a list a numbers is just the difference between the largest and smallest values. Let us understand the concepts better by use of some examples.
The formula for the place to find the median is “([the number of data points] + 1) ÷ 2″, but we don’t have to use this formula. We can just count in from both ends of the list until you meet in the middle, if you prefer, especially if your list is short. The formula works when the number of terms in the series is odd. In case there are even number of numbers, median will be average of two middle numbers in the list.
MEAN VALUE: Mean value refers to the average of a set of values. The simplest way to find the mean is sum of all the values in the set divided by total number of values in the set.
Mean = Sum of all values/total number of values
Example 1: The set S = { 5,10,15,20,30}, Mean of set S = 5+10+15+20+30/5 = 80/5 = 16
Sometimes, the question includes frequency of the values. In that case, the formula changes to
Mean = ∑FiXi / ∑Fi ,
Where, Fi = frequency of the ith value of the distribution, Xi = ith value of the distribution
Example 2: For the given distribution, find the Mean
Xi Fi
1 3
2 5
3 8
4 4
∑Fi= 20
Solution: Mean = (1×3+2×5+3×8+4×4)/20 = 2.65
MEDIAN: Median signifies the central value or the middle value in a sorted list of numbers. To calculate median, the data has to be sorted in ascending or descending order.