Following data reveals the usage of units of electricity by different consumers of a certain area: Units consumed1−5051−100101−150151−200201−250251−300Number of Users(Frequency)24681041268444 Find the following for given data 1. Arithmetic Mean. 2. Median 3. All Quartiles

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Following data reveals the usage of units of electricity by different consumers of a certain area:  Units consumed1−5051−100101−150151−200201−250251−300Number of Users(Frequency)24681041268444  Find the following for given data  1. Arithmetic Mean.  2. Median  3. All Quartiles

Abel Maynard · Accepted Answer

Step 1  Units consumed1−5051−100101−150151−200201−250251−300Number of Users(Frequency)24681041268444  Step 2  1. To find Arithmetic mean   CLASSFrequency(f)MID VALUE(x)d=X−Ahf×fcf1−506825.5−2−1366851−10010475.5−1−104172101−150126125.500298151−20084175.5184382201−25044225.5288426n=426∑f×d=−68  Assumed mean =125.5  Mean =X―=A+∑fdn×h  =125.5+(68)426×50  =125.5−7.9812  =117.5188  Step 3  2. To find Median  =value of(n2)th observation  =value of(4262)th observation  =value of(213)th observation  In cummalative frequency (cf) column (213)-th observation lies in the 101 - 150 class  Therefore median class is 101.5 - 150.5  Now,   L=lower boundary point of median class=100.5  n=total frequency=426  cf=cumulative frequency o the class preceding the median class=172  f=frequency of median class=126  c=class length of median class=50  Median=M=L+n2−cff×c  =100.5+213−172126×50  =100.5+16.2698  =116.7698  Step 4  3. To find All Quartiles  Quartile 1=Q1=class with(n4)th value of the observation in cf column  =(4264)th observation in cf column  (106.5)th observation in cf column  (106.5)th observation lies in 51-100 class

Following data reveals the usage of units of electricity by

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