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The following table shows the number of marks scored by some top students of the world in an international Mathematics competition.

Marks Scored Number of student
1000-2000 20
2000-3000 10
3000-4000 15
4000-5000 30
5000-6000 25
6000-7000 10

What will be the mode of the above data?

 

Option: 1

50


Option: 2

60


Option: 3

30


Option: 4

80


Answers (1)

best_answer

Option (c) 30

The following table shows the number of marks scored by some top students of the world in an international Mathematics competition.

Marks Scored Number of student
1000-2000 20
2000-3000 10
3000-4000 15
4000-5000 30
5000-6000 25
6000-7000 10

Modal class is the class that has the highest frequency.

The highest frequency in the table is 30 which occurs in the interval 4000-5000.

Therefore, the modal class is 4000-5000.

We know the general formula for a mode of grouped data is,

\mathrm{\text{Mode}=L+({\frac{F_{1}-F_{0}}{2F_{1}-F_{0}-F_{2}})\times H}}

Where, the lower limit of the modal class, L = 4000.

Frequency of the modal class, .  \mathrm{{F_{1}=30}}

Frequency of the class preceding the modal class, .\mathrm{ {F_{0}=15}}

Frequency of the class succeeding the modal class, . \mathrm{{F_{2}=25}}

Size of the class interval, H = 1000.

Therefore, from equation (1), we have,

\mathrm{\text{Mode}=4000+({\frac{30-\ 15}{2(30)-\ 15-\ 25})\times 1000}}

\mathrm{\Rightarrow \text{Mode}=4000+({\frac{15}{20})\times 1000} }

\mathrm{\Rightarrow \text{Mode}=4750}

Therefore, the mode of the given data is 4750.

 

 

 

 

Posted by

Deependra Verma

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