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Measure of Central Tendency (Mean, Median, Quartiles and Mode) — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsMeasure of Central Tendency (Mean, Median, Quartiles and Mode)4 Marks
Question
Calculate the mean of the distribution given below using the short cut method.
 
Marks 11 - 20 21 - 30 31 - 40 41 - 50 51 - 60 61 - 70 71 - 80
No. of students 2 6 10 12 9 7 4
✓

Answer

Marks f x d=X-A=X

-45.5		 fd
11-20 2 15.5 -30 -60
21-30 6 25.5 -20 -120
31-40 10 35..5 -10 -100
41-50 12 A=45.5 0 0
51-60 9 55.5 10 90
61-70 7 65.5 20 140
71-80 4 75.5 30 120
  $\Sigma$ f=50     $\Sigma$ fd=70
$\therefore \text { Mean }= A +\frac{\sum f d}{\sum f}$
$=45.5+\frac{70}{50}$
$=45.5+\frac{7}{5}$
$=\frac{227.5+7}{5}$
$=\frac{234.5}{5}$
$=46.9$

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