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Quartiles

The weight of...

Question

The weight of 50 workers is given below:

$\begin{matrix} W e i g h t i n k g & 50 - 60 & 60 - 70 & 70 - 80 & 80 - 90 & 90 - 100 & 100 - 110 & 110 - 120 N u m b e r o f w o r k e r s & 4 & 7 & 11 & 14 & 6 & 5 & 3 \end{matrix}$

Draw an ogive of the given distribution using a graph sheet. Take 2 cm = 10 kg on one axis and 2 cm = 5 workers along the other axis. Use a graph to estimate the upper and lower quartiles.

A

Q₁= 79.1, Q₃ = 96

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B

Q₁= 79.1, Q₃ = 91.1

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C

Q₁= 79.1, Q₃ = 95.1

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D

Q₁= 71.1, Q₃ = 91.1

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Solution

The correct option is D
Q₁= 71.1, Q₃ = 91.1

The cumulative frequency table of the given distribution table is as follows:

$\begin{matrix} H e i g h t (i n c m) & N o . o f s t u d e n t s & c . f . 50 - 60 & 4 & 4 60 - 70 & 7 & 11 70 - 80 & 11 & 22 80 - 90 & 14 & 36 90 - 100 & 6 & 42 100 - 110 & 5 & 47 110 - 120 & 3 & 50 \end{matrix}$

The ogive is as follows:

Number of workers = 50

Lower quartile $(Q_{1}) = (50 / 4)^{t h}$ term $= (12.25)^{t h}$ term=71.1
Upper quartile $(Q_{3}) = (3 \times 50 / 4)^{t h}$ term $= (36.75)^{t h}$ term=91.1

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Q. The weight of 50 workers is given below:

\begin{matrix} W e i g h t i n K g & N o . o f W o r k e r s 50 - 60 & 4 60 - 70 & 7 70 - 80 & 11 80 - 90 & 14 90 - 100 & 6 100 - 110 & 5 110 - 120 & 3 \end{matrix}

Draw an ogive of the given distribution using a graph sheet. Take 2 cm = 10 kg on one axis and 2 cm = 5 workers along the other axis. Use a graph to estimate the following:
(i) the upper and lower quartiles
(ii) If weighing 95 kg and above is considered overweight, find the number of workers who are overweight. [6 MARKS]

Q. The daily wages of

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Use a graph paper to draw an ogive for the above distribution.(Use of scale of

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Wages (in $Rs.$ )	$400 - 450$	$450 - 500$	$500 - 550$	$550 - 600$	$600 - 650$	$650 - 700$	$700 - 750$
No. of workers	$2$	$6$	$12$	$18$	$24$	$13$	$5$

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The median wage of the workers.

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The number of workers who earn more than

Rs. 625

Q. A gas undergoes A to B through three different processes 1, 2 and 3 as shown in the figure. The heat supplied
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S. No.	Wages (Rs.)	S. No.	Wages (Rs.)
1	330	16	240
2	320	17	330
3	550	18	420
4	470	19	380
5	210	20	450
6	500	21	260
7	270	22	330
8	120	23	440
9	680	24	480
10	490	25	520
11	400	26	300
12	170	27	580
13	440	28	370
14	480	29	380
15	620	30	350

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