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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)5 Marks
Question
Marks obtained by 40 students in a short assessment is given below, where a and b are two missing data.
Marks 5 6 7 8 9
Number of Students 6 a 16 13 b
If the mean of the distribution is 7.2, find a and b.
✓

Answer

Marks
(x)		 Number of students
(f)		 fx
5 6 30
6 a 6a
7 16 112
8 13 104
9 b 9b
  $\sum$ f=34+a+b $\sum$ fx=246+6a+9b
It is given that the number of students is 40.
$\therefore 35 + a + b = 40$
$\Rightarrow a + b – 5 = 0 ....(1)$
$\text { Mean }=\frac{\sum f x}{\sum f}$
$\Rightarrow \frac{246+6 a+9 b}{35+a+b}=7.2$
$\Rightarrow 246+6 a+9 b=7.2(35+a+b)$
$\Rightarrow 246+6 a+9 b=252+7.2 a+7.2 b$
$\Rightarrow 0=252-246+7.2 a-6 a+7.2 b-9 b$
$\Rightarrow 6+1.2 a-1.8 b=0$
$\Rightarrow 10+2 a-3 b=0 \ldots . \text { (2) }$
Solving equations (1) and (2), we have
$5a - 5 = 0$
$\Rightarrow a=1$
From (1), we have $b = 4$
Hence, the values of a and b are 1 and 4 respectively.

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