The following frequency distribution gives the monthly consumption of electricity of $68$ consumers of a locality. Find the median, mean and mode of the data and compare them.
Monthly consumption
(in units): $65 - 85$ $85 - 105$ $105 - 125$ $125 - 145$ $145 - 165$ $165 - 185$ $185 - 205$
No. of consumers $4$ $5$ $13$ $20$ $14$ $8$ $4$

Question

The following frequency distribution gives the monthly consumption of electricity of

68

consumers of a locality. Find the median, mean and mode of the data and compare them.

Monthly consumption (in units):	$65 - 85$	$85 - 105$	$105 - 125$	$125 - 145$	$145 - 165$	$165 - 185$	$185 - 205$
No. of consumers	$4$	$5$	$13$	$20$	$14$	$8$	$4$

Filo · Accepted Answer

Classinterval xi​ fi​fi​xi​ Cumulativefrequency 65−85 75 4 300 4 58−10595 5 475 9 105−125115 13 1495 22 125−145 135 20 2700 42 145−165155 14 2170 56 165−185175 8 1400 64 185−205 195 4 780 68   ∑fi​=68  ∑fi​xi​=9320 ⇒  Mean=fi​∑fi​xi​​=689320​=137.05l= lower limit of the modal classh= size of the class intervalsf= frequency of the modal classf1​= frequency of the class preceding the modal classf2​= frequency of the class succeed in the modal class.We have, N=68 and 2N​=34The cumulative frequency just greater than 2N​ is 42 then the median class is 125–145 such that,l=125,h=145–125=20,f=20,cf=22Median=l+f2N​−cf​×h⇒  Median=125+2034−22​×20⇒  Median=125+12=137We know,Mode=l+2f−f1​−f2​f−f1​​×hHere the maximum frequency is 20, then the corresponding class 125–145 is the modal classl=125,h=145–125=20,f=20,f1​=13,f2​=14⇒  Mode=125+13140​=135.77Now, after comparing all three values, we get following relation,Mean>Median>Mode

$Cl a ss in t er v a l$	$x_{i}$	$f_{i}$	$f_{i} x_{i}$	$C u m u l a t i v e f re q u e n cy$
$65 - 85$	$75$	$4$	$300$	$4$
$58 - 105$	$95$	$5$	$475$	$9$
$105 - 125$	$115$	$13$	$1495$	$22$
$125 - 145$	$135$	$20$	$2700$	$42$
$145 - 165$	$155$	$14$	$2170$	$56$
$165 - 185$	$175$	$8$	$1400$	$64$
$185 - 205$	$195$	$4$	$780$	$68$
		$\sum f_{i} = 68$	$\sum f_{i} x_{i} = 9320$

Question Text	The following frequency distribution gives the monthly consumption of electricity of $68$ consumers of a locality. Find the median, mean and mode of the data and compare them.
Answer Type	Text solution:1
Upvotes	150

Text solutionVerified

Practice questions from similar books

The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median, mean and mode of the data and compare them.Monthly consumption(in units):65−8585−105105−125125−145145−165165−185185−205No. of consumers4513201484

Text solutionVerified

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