# How To Calculate The Median From A Histogram?

A histogram tells you how many items fall into each of several bins. The median is the middle item or the average of the two middle items. 1. Find the total number of items represented by the histogram 2. Determine if that number is even or odd. Determine the number of the middle item. 3. Find the bin(s) containing the middle item(s). Example 1   Here is a histogram of test scores, with the number in each bin appended. 51-60 xxx (3) 61-70 xxxxxx (6) 71-80 xxxxxxxx (8) 81-90 xxxx (4) 91-100 xx (2) The total number of scores is 3+6+8+4+2 = 23. Half* the scores (232 = 11) are below the 12th score. The 12th score is in the 71-80 bin, so the median is 71-80. You could use 75 1/2 as a value representative of the bin values if you need to express the result as a single number. Example 2   Suppose the above histogram had (13) in the 91-100 bin. Now there are 34 total scores, of which two are in the middle. The median is on the boundary between the 71-80 bin and the 81-90 bin. You could say the median is 80 1/2.
* When we say half the scores are below the median, we really mean that there are as many scores above the median as there are below the median. In this example, we have 11 scores above the 12th score, and 11 scores below the 12th score. The backslash symbol () is sometimes uses to indicate the integer portion of the result of division. 52 = 2; 5/2 = 2.5
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The median is = value + 1
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A Histogram is a kind of graphical presentation of a continuous series of data.A median is a positional average of a series.To find the median of any given data ,the data should be arranged in ascending and descending order.The formula is
M=l1+(n/2 - c)* I/f
Here l1= lower limit of the middle group;c=cumulative frequency of the preceding group of middle group ;f=frequency of middle group;I = magnitude of middle group.For example
c.I=0-5,5-10,10-15,15-20,20-25,25-30
f  =8  ,7  ,14  ,16  ,9    ,6
c.f=8  ,15  ,29  ,45  ,54    ,60
Here M=value of N/2th item
=60/2
=30 which lies in the group 15-20
M=l1+ (n/2-c)*I/f
=15 +(30-29)*5/16
=15+1*5/16
=15+5/16
=15+0.31
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Equation 1.
Let
a = 5
b = 1
c = 3
(a-b)-c=(5 - 1) -3 =1
but
a-(b-c)=5-(1-3)=5-(-2)
=7
Epuation2
(a-b)-c,
here, -b is a negative number and -c also is.
But in
a-(b-c) when expanded is
a-b+c.
In this case, -b is the only negative number.

Hope this would help.
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