Question

21. Find mode
Class
0-100
Frequency 7
22. There are 5 whit
100-200
21
200-300
37
300-400
13
400-500
12
500-600
10​

Answer 1

Answer:

sorry but really didn't understand your question

Answer 2

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Find the mode of the following frequency distribution:

Class

0-100

100 - 200 200 - 300 300-400 400-500 500 - 600

Frequency

7

21

37

13

12

10

98 A mair of dice is tossed simultaneously

Find the probability that the​

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To Find :-

What is the mode.

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

Solution :-

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

Class Interval

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,

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

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

$\begin{gathered}\dashrightarrow \sf Mode =\: 200 + \dfrac{16}{74 - 34} \times 100\\\end{gathered} ⇢Mode=200+ 74−3416​ ×100​ \begin{gathered}\dashrightarrow \sf Mode =\: 200 + \dfrac{16}{40} \times 100\\\end{gathered} ⇢Mode=200+ 4016​ ×100​ \begin{gathered}\dashrightarrow \sf Mode =\: 200 + \dfrac{160\cancel{0}}{4\cancel{0}}\\\end{gathered} ⇢Mode=200+ 4 0​ 160 0$

$\begin{gathered}\dashrightarrow \sf Mode =\: 200 + \dfrac{\cancel{160}}{\cancel{4}}\\\end{gathered} ⇢Mode=200+ 4​ 160 ​ ​ \begin{gathered}\dashrightarrow \sf Mode =\: 200 + 40\\\end{gathered} ⇢Mode=200+40​ \dashrightarrow \sf\bold{\red{Mode =\: 240}}⇢Mode=240\therefore∴ The mode is 240.\rule{150}{2}$

IMPORTANT FORMULA :

♣ 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,

$\sf \Sigma f_ix_iΣf i​ x i​ = Sum of all the observations\sf \Sigma f_iΣf i$

= Sum of frequencies or observations

♣ Median Formula :

$\begin{gathered}\longmapsto \sf\boxed{\bold{\pink{Median =\: l + \bigg\lgroup \dfrac{\frac{n}{2} - cf}{f}\bigg \rgroup \times h}}}\\\end{gathered} ⟼ Median=l+ ⎩⎪⎪⎪⎧​ f2n​ −cf​ ⎭⎪⎪⎪⎫​ ×h$

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)