Explanation
Median= 45 + [{(330/2) – 124}/76] × 15
Median is the middle most value of a series. So when the series has odd number of elements then median can be calculated easily but when the series has even number of elements then the series has two middle values, so median is calculated by taking out the average of both the value.
The series is first arranged into either ascending or descending order. The formula to calculate median = (N+1) /2 th term of the series where N is the number of observation in the series.
The given series is first arranged into ascending; 10,14,15,16,18,18,18,19,20,22,23.
N= 11
median= (11+1)/2 th term = 12/2 th term = 6 th term = 18
Class Intervals
0−10
10−20
20−30
30−40
Frequency(f)
8
10
12
15
Class mark ( mid points= x)
5
25
35
Fx
40
150
300
525
Mean = summation of fx / summation of f
= 1015/ 45
= 22.55
Marks
No. of Students
4.5 −14.5
14.5 −24.5
18
24.5 −34.5
32
34.5 −44.5
26
44.5−54.5
14
54.5−64.5
Median= 24.5 + [{(110/2) – 28}/32] × 10
The given series is first arranged into ascending; 15,20,30,36,45,60.
N= 6
median= (6+1)/2 th term = 7/2 th term = 3.5 th term
= ( value of 3rd term + value of 4th term)/2
= (30+36) /2 = 66/2 =33
Positional average refers to the average which are taken out through observation from the series where a particular value from the series is picked up which represents the whole series.
In mean, the average of the whole series of observation is taken. In median, the middle most value of the series is taken whereas in mode, the value which occurs the highest number of times is taken as the representative value.
The series is first arranged into either ascending or descending order. The formula to calculate median = (N+1) /2 th term of the series in case odd numbers of data and median = N/2th term of the series in case even number of data where N is the number of observation in the series.
Mean refers to the average amount in a given group of data. There are many ways to calculate arithmetic mean like direct method where all the data are added up and then divided by the number of figures in the data in order to ascertain the mean class or assumed mean method and step deviation method, the data of the given class is reduced into smaller units which makes it easy to do calculation and ascertain the mean of the class.
i.e.
The given series is first arranged into ascending; 1,2,2,3,4,5,6,7,8,9
N= 10
median= (10+1)/2 th term = 11/2 th term = 5.5 th term
= ( value of 5th term + value of 6th term)/2
= (4+5) /2 = 9/2 = 4.5
The given series is first arranged into ascending; 29,32,48,50,x,x+2,72,78,84,95
median=> (10+1)/2 th term = 63
=> 11/2 th term = 63
=> 5.5 th term = 63
=> ( value of 5th term + value of 6th term)/2= 63
=> {x+( x+2)} /2 =63
=> 2x+2 = 126
=> 2x = 124
=> x= 62
$$\Rightarrow $$mean =$$\dfrac {(15\times 2)+(17\times 3)+(19 \times 4)+((20+p) \times 5p)+(23 \times 6)}{2+3+4+5p+6}$$
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