The following table shows the profits earned by companies in lakhs of rupees.

Profit 5-10 10-15 15-20 20-25 25-30

No. of companies 4 28 49 17 2

Draw a histogram and determine the mode.

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Solution

(i) Draw a histogram to represent the given data.
(ii) Locate the modal class , pre-modal class and post-modal class.
(iii) Join the right-hand top vertices of modal class (C) and pre-modal class (A) by a straight line .
(iv) Join the left-hand top vertices of modal class (B) and post-modal class (D) by a straight line .
(v) Let the point of intersection of AC and BD be E .
(vi) Draw a segment EF perpendicular to the X-axis .
(vii) The foot of perpendicular, F, is the mode .

The histogram showing the mode graphically is drawn below.

The mode can also be verified using the formula for calculating mode.
Here, L = 15, f_m= 49, f₁ = 28, f₂ = 17 , h = 5

$Therefore, mode = L + [\frac{f_{m} - f_{1}}{2 f_{m} - f_{1} - f_{2}}] h = 15 + [\frac{49 - 28}{2 \times 49 - 28 - 17}] \times 5 = 15 + \frac{105}{53} = 16.98$

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Similar questions

Profit	$5 - 10$	$10 - 15$	$15 - 20$	$20 - 25$	$25 - 30$
No. of companies	$4$	$28$	$49$	$17$	$2$

Profits (₹ in Lakhs)	10−20	20−30	30−40	40−50	50−60	60−70
No. of Companies	4	7	10	20	17	2

Year	1995-96	1996-97	1997-98	1998-99	1999-2000
Interest (in lakhs of rupees)	20	25	15	18	30

Class Interval	0−5	5−10	10−15	15−20	20−25	25−30
Frequency	20	24	32	28	20	26

Marks:	0-5	5-10	10-15	15-20	20-25	25-30	30-35
No. of students	2	6	13	17	11	4	2

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