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Mean, Median, Mode of Grouped Data — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsMean, Median, Mode of Grouped Data2 Marks
Question
Find the mean of the following frequency distribution using step-deviation method:
Class
84-90
90-96
96-102
102-108
108-114
114-120
Frequency
15
22
20
18
20
25
✓

Answer

Class interval
Frequency $f_i$
Mid values $x_i$
 $\text{u}_\text{i}=\frac{\text{x}_\text{i}-\text{A}}{\text{h}}=\frac{\text{x}_i-99}{6}$
$f_i \times u_i$
84-90
15
87
 -2
-30
90-96
 22
93
 -1
-22
96-102
 20
99 = A
 0
0
102-108
18
105
 1
18
108-114
20
111
 2
40
114-120 25 117 3 75
  $\sum\text{f}_\text{i}=120$     $\sum\text{f}_\text{i}\text{u}_\text{i}=81$
Thus, $\text{A}=99,\ \text{h}=6,\ \sum\text{f}_\text{i}=120$ and $\sum\text{f}_\text{i}\text{u}_\text{i}=81$
Mean $=\text{A}+\Big\{\text{h}\times\frac{\sum\text{f}_\text{i}\text{u}\text{i}}{\sum\text{f}_\text{i}}\Big\}$
$=99+\Big\{6\times\frac{81}{120}\Big\}$
$=99+4.05$
$=103.05$

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