1Find \( Q_1 \) and \( Q_3 \) from the data: 10, 12, 14, 11, 22, 15, 27, 14, 16, 13, 25
2Find \( Q_1 \) and \( Q_3 \): the marks 42, 48, 49, 53, 56, 59, 60, 65, 68, 70 were obtained by 2, 3, 5, 8, 9, 11, 7, 8, 6, 4 students, in that order.
3Find \( Q_1 \) and \( Q_3 \) for the ages of students in years, with the number of students in brackets: 2-4 (5), 4-6 (12), 6-8 (25), 8-10 (26), 10-12 (24), 12-14 (28), 14-16 (20), 16-18 (15).
4Find \( Q_1 \) and \( Q_3 \) for these marks, with the number of students in brackets: 10-20 (2), 20-30 (3), 30-40 (6), 40-50 (12), 50-60 (13), 60-70 (11), 70-80 (7).
5Find \( Q_1 \) and \( Q_3 \) for these heights in cm, with the number of students in brackets: 100-110 (3), 110-120 (4), 120-130 (9), 130-140 (15), 140-150 (20), 150-160 (14), 160-170 (7).
6Find \( Q_1 \) and \( Q_3 \) for these daily wages in rupees, with the number of workers in brackets: 100-150 (6), 150-200 (11), 200-250 (21), 250-300 (34), 300-350 (25), 350-400 (22).
7Find \( Q_1 \) and \( Q_3 \) for these marks, with the frequency in brackets: 0-20 (8), 20-40 (12), 40-60 (15), 60-80 (14), 80-100 (12), 100-120 (9), 120-140 (10).
8Find \( Q_1 \) and \( Q_3 \) for these times in minutes, with the frequency in brackets: 0-10 (5), 10-20 (3), 20-30 (10), 30-40 (6), 40-50 (4), 50-60 (2).
9Find \( Q_1 \) and \( Q_3 \) for these times in minutes, with the frequency in brackets: 20-25 (2), 25-30 (5), 30-35 (8), 35-40 (6), 40-45 (4), 45-50 (5).
10If \( Q_1 = 8 \), what is the value of \( k \)? Ages in years, with the number of pupils in brackets: 0-6 (9), 6-12 (6), 12-18 (5), 18-24 (\( k \)), 24-30 (7), 30-36 (9).
11If \( Q_1 = 31 \), what is the missing frequency? Class intervals with frequency in brackets: 10-20 (4), 20-30 (5), 30-40 (?), 40-50 (8), 50-60 (7), 60-70 (6).
12If \( Q_1 = 51.75 \), what is the value of \( q \)? Weights in kg, with frequency in brackets: 40-44 (8), 44-48 (10), 48-52 (14), 52-56 (\( q \)), 56-60 (3), 60-64 (1).
13Find \( Q_1 \) and \( Q_3 \). Heights of students: less than 125 cm: 0, less than 130: 5, less than 135: 11, less than 140: 24, less than 145: 45, less than 150: 60, less than 155: 72.
14Find \( Q_1 \) and \( Q_3 \) for these weights in lbs, with frequency in brackets: 110-119 (5), 120-129 (7), 130-139 (12), 140-149 (20), 150-159 (16), 160-169 (10), 170-179 (7), 180-189 (3).
15Find \( Q_1 \) and \( Q_3 \) for daily expenditure in rupees, with frequency in brackets: less than 100 (22), 100-200 (34), 200-300 (52), 300-400 (20), 400-500 (19), more than 500 (13).
16Find \( Q_1 \) and \( Q_3 \). Marks obtained: less than 20: 21 students, less than 40: 44, less than 60: 66, less than 80: 79, less than 100: 90.
17The marks of 30 students in an internal examination are: 42, 65, 78, 70, 62, 50, 72, 34, 30, 40, 58, 53, 30, 34, 51, 54, 42, 59, 20, 40, 42, 60, 25, 35, 35, 28, 46, 60, 47, 52. Make a table with a class interval of 10 and find the first and third quartiles.
18The numbers of eggs produced each day in a chicken farm are: 32, 87, 17, 51, 99, 79, 64, 39, 25, 95, 53, 49, 78, 32, 42, 48, 59, 86, 69, 57, 15, 27, 44, 66, 77, 92. Make a table with a class interval of 20 and find the first and third quartiles.
19Using the marks of 60 students in Example 2, find the second quartile \( Q_2 \).
20For the marks of 200 students, \( Q_1 = 45 \) and \( Q_3 = 70 \). About how many students scored between 45 and 70? Give a reason.
21A student found \( Q_1 \) of a continuous series using the position \( \frac{N+1}{4} \). What went wrong, and what should the position be?