Question

Find the mode of the following frequency distribution :
class frequency
0-100 - 7

100-200 - 21

200-300 - 37

300-400 - 13

400-500 - 12

500-600 - 10​

Answer 1

The mode of the given table is 204

Answer 2

${\huge{\boxed{\sf{\yellow{❥✰Question✰}}}}}$

Find the mode of the following frequency distribution :

class frequency

0-100 - 7

100-200 - 21

200-300 - 37

300-400 - 13

400-500 - 12

500-600 - 10​

$\huge\mathbb\fcolorbox{purple}{Green}{☆AnSwER♡}$

Hence, the correct options is option no (D) 20 cm/s².

$\huge\mathbb\fcolorbox{Green}{violet}{♡Soltution}$

Given :-

• A particle is describing uniform circular motion on a circle of radius of 5 cm with speed of 10 cm/s.

To Find :-

• What is the centripetal acceleration.

Formula Used :-

Mode Formula :

$\begin{gathered}\longmapsto \sf\boxed{\bold{\pink{Mode =\: l + \dfrac{f_1 - f_0}{2f_1 - f_0 - f_2} \times h}}}\\\end{gathered} ⟼ Mode=l+ 2f 1​ −f 0​ −f 2​ f 1​ −f 0​ ​ ×h$

Where l =

Lower limit of modal class

f₁ = Frequency of the model class

f₀ = Frequency of the class preceding the model class

f₂ = Frequency of the class succeeding the model class

h = Size of the class interval

$\Huge \fbox{{\color{Full}{\textsf {\textbf {Solution :-}}}}}$

$\begin{gathered}\boxed{\begin{array}{cccc}\sf Class\: Interval&\sf Frequency\\\frac{\qquad \qquad \qquad \qquad}{} &\frac{\qquad \qquad \qquad \qquad \qquad}{}\\\sf 0-100&\sf 7\\\\\sf 100-200&\sf 21\\\\\sf 200-300&\sf 37\\\\\sf 300-400&\sf 13\\\\\sf 400-500&\sf 12\\\\\sf 500-600&\sf 10\end{array}}\end{gathered}$

Given :

Lower limit of modal class (l) = 200

Frequency of the modal class (f₁) = 37

Frequency of the class preceding the model class (f₀) = 21

Frequency of the class succeeding the model class (f₂) = 13

Size of the class interval (h) = 300 - 200 = 100

According to the question by using the formula we get,

$\begin{gathered}\dashrightarrow \sf Mode =\: 200 + \dfrac{37 - 21}{2(37) - 21 - 13} \times 100\\\end{gathered} ⇢Mode=200+ 2(37)−21−1337−21​ ×100$

$\begin{gathered}\dashrightarrow \sf Mode =\: 200 + \dfrac{16}{2 \times 37 - 34} \times 100\\\end{gathered} ⇢Mode=200+ 2×37−3416​ ×100$

$\begin{gathered}\dashrightarrow \sf Mode =\: 200 + \dfrac{16}{74 - 34} \times 100\\\end{gathered} ⇢Mode=200+ 74−3416​ ×100$

$\begin{gathered}\dashrightarrow \sf Mode =\: 200 + \dfrac{16}{40} \times 100\\\end{gathered} ⇢Mode=200+ 4016​ ×100$

$\begin{gathered}\dashrightarrow \sf Mode =\: 200 + \dfrac{160\cancel{0}}{4\cancel{0}}\\\end{gathered} ⇢Mode=200+ 4 0​ 160 0$

$\begin{gathered}\dashrightarrow \sf Mode =\: 200 + \dfrac{\cancel{160}}{\cancel{4}}\\\end{gathered} ⇢Mode=200+ 4​ 160$

$\begin{gathered}\dashrightarrow \sf Mode =\: 200 + 40\\\end{gathered} ⇢Mode=200+40$

$\dashrightarrow \sf\bold{\red{Mode =\: 240}}⇢Mode=240$

The mode is 240.

IMPORTANT FORMULA :

$\clubsuit♣$ Mean Formula :

$\begin{gathered}\longmapsto \sf\boxed{\bold{\pink{Mean =\: \dfrac{\Sigma f_ix_i}{\Sigma f_i}}}}\\\end{gathered} ⟼ Mean= Σf i​ Σf i​ x i$

where,

$\sf \Sigma f_ix_iΣf i​ x i$

 = Sum of all the observations

 = Sum of frequencies or observations

$\clubsuit♣$ Median Formula :

$\begin{gathered}\longmapsto \sf\boxed{\bold{\pink{Median =\: l + \bigg\lgroup \dfrac{\frac{n}{2} - cf}{f}\bigg \rgroup \times h}}}\\\end{gathered} ⟼ Median=l+$

where,

l = Lower limit of median class

n = Number of Observations

cf = Cumulative frequency of the class preceding the median class

f = Frequency of median class

h = Size of the class interval (assuming class are of equal size)