what is mode,mean,mediun full explanation with example. wrong answer will be reported and delete his all questions and answers
Answers
Mean Median Mode Formula
The Mean, Median and Mode are the three measures of central tendency. Mean is the arithmetic average of a data set. This is found by adding the numbers in a data set and dividing by the number of observations in the data set. The median is the middle number in a data set when the numbers are listed in either ascending or descending order. The mode is the value that occurs the most often in a data set and the range is the difference between the highest and lowest values in a data set.
The Mean
x¯¯¯=∑xN
Here,
$\sum$ represents the summation∑ represents the summation
X represents observations
N represents the number of observations .
The Median
If the total number of observations (n) is an odd number, then the formula is given below:
Median=(n+12)thobservation
If the total number of the observations (n) is an even number, then the formula is given below:
Median=(n2)thobservation+(n2+1)thobservation2
The Mode
Themodeisthemostfrequentlyoccuringobservationorvalue.
Solved Examples
Question: Find the mean, median, mode, and range for the following list of values:
13, 18, 13, 14, 13, 16, 14, 21, 13
Solution:
Given data: 13, 18, 13, 14, 13, 16, 14, 21, 13
The mean is the usual average.
Mean = 13+18+13+14+13+16+14+21+139=15
(Note that the mean is not a value from the original list. This is a common result. You should not assume that your mean will be one of your original numbers.)
The median is the middle value, so to rewrite the list in ascending order as given below:
13, 13, 13, 13, 14, 14, 16, 18, 21
There are nine numbers in the list, so the middle one will be
9+12=102=5
= 5th number
Hence, the median is 14.
The mode is the number that is repeated more often than any other, so 13 is the mode.
The largest value in the list is 21, and the smallest is 13, so the range is 21 – 13 = 8.
Mean = 15
Median = 14
Mode = 13
Range = 8
Mode:
Mode is the number that occurs the maximum number of times.
Examples
Ex 1:
1,5,6,7,6,8,9,0
Here mode is 6 since 6 is repeated maximum number of times.(2 times)
Ex 2 :
8,2,5,6,8,6,7,0
Here mode is 8 and 6 because they are repeated maximum number of times(2 times)
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Mean:
Mean is the average value of a group of observations in a given data.
Mean formula
Mean = Sum of observations/ no of observations
Examples:
Ex 1 : Find mean of 2,3,5,6
We know that,
Mean = Sum of observations/ no of observations
Mean = 2+3+5+6 / 4 = 16/4 = 4
Therefore, mean is 4
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Median :
Median is the value of the middle observation when data is in ascending order or descending order.
Median formula (when no of observations is odd)
Median = n+1/2
Median formula (when no of observations is even
Median = 1/2 ((n/2 th) + (n/2 + 1 th))
Examples
Ex 1 :
Find median of 10, 10, 13, 10, 14, 11, 9
Ascending order of observations:
9, 10, 10, 10, 11, 13, 14
No of observations = 7
We know that
Median = n+1/2
Median = 7 + 1 / 2 th = 8/ 2 th = 4th
Therefore,median is 4th observation which is 10
Ex 2 :
Find median of 10, 10, 13, 10, 14, 11, 9, 12
Ascending order of observations:
9, 10, 10, 10, 11, 12, 13, 14
No of observations = 8
We know that
Median = 1/2 ((n/2 th) + (n/2 + 1 th))
= 1/2 ((8/2th) + (8/2 + 1 th))
= 1/2 ((4th) + (4 + 1 th))
= 1/2 ((4th) + ( 5th))
= 1/2 (10 + 11)
= 1/2 (21)
= 21/2
= 10.5
Therefore 10.5 is median
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