The following data gives the marks obtained by students in an exam-WlineBelow - 10 - 5 WlhlineBelow 20 - 10 Wlhline Below 30 - 23 Whline Below 40 - 31 WhlineBelow 50 - 45 wlhlineBelow 60 - 49 Wlhline array iConvert the cumulative distribution to a regular distribution-iiCalculate the mode- -3 MARKS-

Table: 1 Mark Application: 2 Marks [ Class Interval amp;Frequency; 0 10 amp; 5; 10 20 amp; 5; 20 30 amp; 13 ...

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Standard X

Mathematics

Grouped Frequency Table

The following...

Question

The following data gives the marks obtained by students in an exam.

$\begin{matrix} Class interval & Frequency B e l o w 10 & 5 B e l o w 20 & 10 B e l o w 30 & 23 B e l o w 40 & 31 B e l o w 50 & 45 B e l o w 60 & 49 \end{matrix}$

(i)Convert the cumulative distribution to a regular distribution.

(ii)Calculate the mode. [3 MARKS]

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Solution

Table: 1 Mark
Application: 2 Marks

$\begin{matrix} Class Interval & Frequency 0 - 10 & 5 10 - 20 & 5 20 - 30 & 13 30 - 40 & 8 40 - 50 & 14 50 - 60 & 4 \end{matrix}$

Mode
$= I + (\frac{f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2}}) \times h$

$= 20 + \frac{13 - 5}{26 - 5 - 8} \times 10$

$= 26.15$

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Q. Question 10
The following table shows the cumulative frequency distribution of marks of 800 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 B e l o w 10 & 10 B e l o w 20 & 50 B e l o w 30 & 130 B e l o w 40 & 270 B e l o w 50 & 440 B e l o w 60 & 570 B e l o w 70 & 670 B e l o w 80 & 740 B e l o w 90 & 780 B e l o w 100 & 800 \end{matrix}

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The following data gives the marks obtained by students in an exam. Class intervalFrequencyBelow 105Below 2010Below 3023Below 4031Below 5045Below 6049 (i)Convert the cumulative distribution to a regular distribution. (ii)Calculate the mode. [3 MARKS]

Table: 1 Mark Application: 2 Marks Class IntervalFrequency0−10510−20520−301330−40840−501450−604 Mode =I+(f1−f02f1−f0−f2)×h =20+13−526−5−8×10 =26.15

Table: 1 Mark
Application: 2 Marks

$\begin{matrix} Class Interval & Frequency 0 - 10 & 5 10 - 20 & 5 20 - 30 & 13 30 - 40 & 8 40 - 50 & 14 50 - 60 & 4 \end{matrix}$

Mode
$= I + (\frac{f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2}}) \times h$

$= 20 + \frac{13 - 5}{26 - 5 - 8} \times 10$

$= 26.15$