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

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

$= 26.15$