The following distribution represents the height of 160 students of some school- beginarray - c - c -Wline Height - in - cm -Number of studentsllthline 140-145-12 11 hline 145-150820 ll hline 150-155 - 30 Wlhline 155-160-3811 hline 160-165-2411 Hhine170-175 - 12 Whline175-18088 Winlinearray 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-A- 157 cm approxB- 167 cm approxC- 150 cm approxD- 159 cm approx

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Byju's Answer

Standard X

Mathematics

Median

The following...

Question

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.

150 cm (approx)

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159 cm (approx)

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157 cm (approx)

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167 cm (approx)

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Solution

The correct option is C
157 cm (approx)

Taking scale as 2cm=5 cm on x-axis and 2cm=20 students on the y- axis. Ogive for the given distribution is as follows:

$\begin{matrix} H i g h t (i n c m) & N o . o f s t u d e n t s & c . f . 140 - 145 & 12 & 12 145 - 150 & 20 & 32 150 - 155 & 30 & 62 155 - 160 & 38 & 100 160 - 165 & 24 & 124 165 - 170 & 16 & 140 170 - 175 & 12 & 152 175 - 180 & 8 & 160 \end{matrix}$

Median Height = (N/2)th observation

= (160/2)^th observation

= 80^th observation

= 157 cm (Approx)

Suggest Corrections

Similar questions

Q. 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

Q. Given below is the frequency distribution of the heights of 50 students of a class:

\begin{matrix} Class Interval & 140 - 145 & 145 - 150 & 150 - 155 & 155 - 160 & 160 - 165 Frequency & 8 & 12 & 18 & 10 & 5 \end{matrix}

Draw a histogram representing the above data.

Q. Given below is the frequency distribution of the heights of 50 students of a class:

Class interval:	140−145	145−150	150−155	155−160	160−165
Frequency:	8	12	18	10	5

Draw a histogram representing the above data.

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.

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.

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