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Standard VIII

Mathematics

Scale Factor

The following...

Question

The following distribution represent the height of $160$ students of a school.
Height (in $c m$ ) No. of Students
$140 - 145$ $12$
$145 - 150$ $20$
$150 - 155$ $30$
$155 - 160$ $38$
$160 - 165$ $24$
$165 - 170$ $16$
$170 - 175$ $12$
$175 - 180$ $8$
Draw an ogive for the given distribution taking $2 c m = 5 c m$ of height on one axis and $2 c m = 20$ students on the other axis. Using the graph, determine:
(i) The median height
(ii) The inter quartile range
(iii) The number of students whose height is above $172 c m$ .

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Solution

Height (cm) Frequency of students Cumulative
$140 - 145$ $12$ $12$
$145 - 150$ $20$ $32$
$150 - 155$ $30$ $62$
$155 - 160$ $38$ $108$
$160 - 165$ $24$ $124$
$165 - 170$ $16$ $140$
$170 - 175$ $12$ $152$
$175 - 180$ $8$ $160$
Median $= 157$
Inter quartile $= 164 - 152$
Height above 172cm $= 12$

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Similar questions

The following distribution represents the height of 160 students of some school.

$\begin{matrix} H e i g h t (i n c m) & N u m b e r o f s t u d e n t s 140 - 145 & 12 145 - 150 & 20 150 - 155 & 30 155 - 160 & 38 160 - 165 & 24 165 - 170 & 16 170 - 175 & 12 175 - 180 & 8 \end{matrix}$

Draw an ogive for the given distribution taking 2 cm = 5 cm of height on one axis and 2 cm = 20 students on the other axis. Using the graph, determine the median height.

The following table shows the distribution of the heights of a group of factory workers :

$\begin{matrix} Ht. (cm): & 150 - 155 & 155 - 160 & 160 - 165 & 165 - 170 & 170 - 175 & 175 - 180 & 180 - 185 No. of workers & 6 & 12 & 18 & 20 & 13 & 8 & 6 \end{matrix}$

(i) Determine the cumulative frequencies.

(ii) Draw the 'less than' cumulative frequency curve on graph paper. Use 2 cm = 5 cm height on one axis and 2 cm = 10workers on the other.

Q. Consider the frequency distribution of the height of clan:-
Find median class

Height $c m$	$150 - 155$	$155 - 160$	$160 - 165$	$165 - 170$	$170 - 175$	$175 - 180$
No of student	$16$	$12$	$9$	$7$	$10$	$6$
Cummulative frequency	$16$	$28$	$37$	$44$	$54$	$60$

Q. Use Graph paper for this question. A Survey regarding height (in cm ) of

60

boys belonging to Class

10

of a school was conducted. The following data was recorded.

Height in cm	$135 - 140$	$140 - 145$	$145 - 150$	$150 - 155$	$155 - 160$	$160 - 165$	$165 - 170$
No. of boys	$4$	$8$	$20$	$14$	$7$	$6$	$1$

Taking

2

=

height of

10

cm along one axis and

2

= 10

boys along the other axis draw an ogive of the distribution. Use the graph to estimate the median.

Q. Use Graph paper for this question.
A survey regarding height(in cm) of

60

boys belonging to Class

10

of a school was conducted. The following data was recorded.

Height in cm	$135 - 140$	$140 - 145$	$145 - 150$	$150 - 155$	$155 - 160$	$160 - 165$	$165 - 170$
No. of boys	$4$	$8$	$20$	$14$	$7$	$6$	$1$

Taking

2

=

height of

10

cm along one axis and

2

= 10

boys along the other axis draw an ogive of the above distribution. Use the graph to estimate the Lower Quartile.

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Height (in $c m$ )	No. of Students
$140 - 145$	$12$
$145 - 150$	$20$
$150 - 155$	$30$
$155 - 160$	$38$
$160 - 165$	$24$
$165 - 170$	$16$
$170 - 175$	$12$
$175 - 180$	$8$

Height (cm)	Frequency of students	Cumulative
$140 - 145$	$12$	$12$
$145 - 150$	$20$	$32$
$150 - 155$	$30$	$62$
$155 - 160$	$38$	$108$
$160 - 165$	$24$	$124$
$165 - 170$	$16$	$140$
$170 - 175$	$12$	$152$
$175 - 180$	$8$	$160$

Height (cm) Frequency of students Cumulative 140−145 12 12 145−150 20 32 150−155 30 62 155−160 38 108 160−165 24 124 165−170 16 140 170−175 12 152 175−180 8 160Median =157Inter quartile =164−152Height above 172cm =12

Height (cm) Frequency of students Cumulative
$140 - 145$ $12$ $12$
$145 - 150$ $20$ $32$
$150 - 155$ $30$ $62$
$155 - 160$ $38$ $108$
$160 - 165$ $24$ $124$
$165 - 170$ $16$ $140$
$170 - 175$ $12$ $152$
$175 - 180$ $8$ $160$
Median $= 157$
Inter quartile $= 164 - 152$
Height above 172cm $= 12$