The following table shows marks secured by 140 students in an examination-WlineMarks - Number of students Wline0-10 - 20 1Wline 10-20 - 24 Wline 20-30 - 40 1Wline30-40 - 36 Wline40-50 - 20 1Wline array Calculate mean marks by the step deviation method-A- 25B- 25-86C- 26-92D- 20-4

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Standard XI

Statistics

Mean of Continuous Series

The following...

Question

The following table shows marks secured by 140 students in an examination:

$\begin{matrix} M a r k s & N u m b e r o f s t u d e n t s 0 - 10 & 20 10 - 20 & 24 20 - 30 & 40 30 - 40 & 36 40 - 50 & 20 \end{matrix}$

Calculate mean marks by the step deviation method.

20.4

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25.86

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26.92

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Solution

The correct option is C 25.86
Let:
Number of students = $f_{i}$
Mid-value of marks = $x_{i}$
$u_{i} = \frac{(x_{i} - 25)}{10}$

$\begin{matrix} M a r k s & f_{i} & x_{i} & u_{i} & f_{i} u_{i} 0 - 10 & 20 & 5 & - 2 & - 40 10 - 20 & 24 & 15 & - 1 & - 24 20 - 30 & 40 & 25 (= a) & 0 & 0 30 - 40 & 36 & 35 & 1 & 36 40 - 50 & 20 & 45 & 2 & 40 T o t a l & 140 & 12 \end{matrix} M e a n = a + 10 \times \frac{\sum f_{i} u_{i}}{\sum f_{i}} = 25 + 10 \times \frac{12}{140} = 25.86$

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Similar questions

The following table shows marks secured by 140 students in an examination:
$\begin{matrix} M a r k s & N u m b e r o f s t u d e n t s 0 - 10 & 20 10 - 20 & 24 20 - 30 & 40 30 - 40 & 36 40 - 50 & 20 \end{matrix}$
Calculate mean marks by the step deviation method.

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Q. The marks obtained by 40 students of class X in math paper of 50 marks total, are presented in the table. Find the mean using direct method.

\begin{matrix} Marks obtained & Number of students 0 - 10 & 3 10 - 20 & 4 20 - 30 & 13 30 - 40 & 15 40 - 50 & 5 \end{matrix}

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The following table shows marks secured by 140 students in an examination: MarksNumber of students0−102010−202420−304030−403640−5020 Calculate mean marks by the step deviation method.

The correct option is C 25.86Let: Number of students = fi Mid-value of marks = xi ui=(xi−25)10 Marksfixiuifiui0−10205−2−4010−202415−1−2420−304025(=a)0030−40363513640−502045240Total14012Mean=a+10×∑fiui∑fi=25+10×12140=25.86

The following table shows marks secured by 140 students in an examination:

$\begin{matrix} M a r k s & N u m b e r o f s t u d e n t s 0 - 10 & 20 10 - 20 & 24 20 - 30 & 40 30 - 40 & 36 40 - 50 & 20 \end{matrix}$

Calculate mean marks by the step deviation method.