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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
Using step- deviation method , calculate the mean marks of the following distribution.
 
C.I 50-55 55-60 60-65 65-70 70-75 75-80 80-85 85-90
Frequency 5 20 10 10 9 6 12 8
✓

Answer

Let the assumed mean A=72.5
C.I $f_i$ Mid-value

$(x_i)$		 A=72.5

t=(x-A)/(i)		 $f_it_i$
50-55 5 52.5 -4 -20
55-60 20 57.5 -3 -60
60-65 10 62.5 -2 -20
65-70 10 67.5 -1 -10
70-75 9 72.5 0 0
75-80 6 77.5 1 6
80-85 12 82.5 2 24
85-90 8 87.5 3 24
Total 80     -56
$\text { Mean }= A +\frac{ f _{ i } t _{ i }}{ n } \times i$
$=72.5+\left(-\frac{56}{80}\right) \times 5$
$=72.5-0.7 \times 5$
$=72.5-3.5$
$=69$

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