Question

The following distribution represents the number of books issued at the counter of a ecommerce college library on $200$ different days :
Calculate lower and upper quartile for above data.

No. of books issued	$80$	$100$	$120$	$145$	$200$	$280$	$310$	$380$	$400$	$410$
No. of days	$15$	$18$	$25$	$27$	$40$	$25$	$19$	$16$	$8$	$7$

Answer 1

The given distribution represents the no. of books issued at the counter of a ecommerce college library on 200 distribution

No of books issued	80	100	120	145	200	280	310	380	400	410
No. of days	15	18	25	27	40	25	19	16	8	7

Lower and upper quartile

No.mof books issued	No. of days (Freqvency)	Cumulative frequency
80	15	15
100	18	15 $+$ 18 $=$ 33
120 (lower quartile)	25	33 $+$ 25 $=$ 58
145	27	58 $+$ 27 $=$ 85
200	40	85 $+$ 40 $=$ 125
280	25	125 $+$ 25 $=$ 150
310	19	150 $+$ 19 $=$ 169
380 (upper quartile)	16	169 $+$ 16 $=$ 185
400	8	185 $+$ 8 $=$ 193
410	7	193 $+$ 7 $=$ 200

$N=200$

Lower qualtile $\left(Q_1\right)=\text{size of}\frac{N+1}{4}th\text{item}$

$=\text{size of}\frac{200+1}{4}th\text{item}$
$=\text{size of}\frac{201}{4}th\text{item}$

$=\text{size of}{50.25}^{th}\text{item}$

So, Lower quartile $\left(Q_1\right)=120$

Upper quartile $\left(Q_3\right)=\text{size of}\frac{3(N+1)}{4}th\text{item}$

$=\text{size of}\frac{3(200+1)}{4}th\text{item}$

$=\text{size of}3(50.25{)}^{th}\text{item}$

$=\text{size of}{150.75}^{th}\text{item}$

$\left(Q_3\right)=280$