Determine the mode of the following grouped frequency distribution: <style> table{width:100%;margin-bottom:5px; margin-top:5px;} table, th, td { border: 1px solid black; border-collapse: collapse; text-align: center;} </style> <table><tr> <td>Class Interval</td><td>3-6</td><td>6-9</td><td>9-12</td> </tr><tr> <td>Frequency</td><td>2</td><td>6</td><td>12</td> </tr></table> <table><tr> <td>12-15</td><td>15-18</td><td>18-21</td><td>21-24</td> </tr><tr> <td>24</td><td>21</td><td>12</td><td>3</td> </tr></table>

Q.Determine the mode of the following grouped frequency distribution:

Class Interval	3-6	6-9	9-12
Frequency	2	6	12

12-15	15-18	18-21	21-24
24	21	12	3

The modal class of the given frequency distribution is 12-15. ∴ The required mode \[ = l + \left(\cfrac{f_1-f_0}{2f_1-f_0-f_2}\right) \times h \] where \( l = 12, f_1 = 24, f_0 = 12, f_2 = 21, h = 3 \) \[ = 12 + \cfrac{24-12}{2\times24 -12 -21} \times 3 \] \[ = 12 + \cfrac{12}{15} \times 3 \] \[ = 12 + \cfrac{12}{5} \] \[ = 12 + 2.4 \] \[ = 14.4 \, (\text{approx}) \]

Class Interval	0-5	5-10	10-15	15-20	20-25	25-30	30-35
Frequency	5	12	18	28	17	12	8

15-20	20-25	25-30	30-35
28	17	12	8

15-20	20-25	25-30	30-35
28	17	12	8

15-20	20-25	25-30	30-35
28	17	12	8

Marks	Less than 10	Less than 20	Less than 30	Less than 40	Less than 50	Less than 60	Less than 70	Less than 80
Number of students	4	16	40	76	96	112	120	125

Class Boundaries	Less than 10	Less than 20	Less than 30	Less than 40	Less than 50	Less than 60	Less than 70	Less than 80
Frequency	4	16	40	76	96	112	120	125

Class Interval	0 - 10	10 - 20	20 - 30	30 - 40	40 - 50	50 - 60
Frequency	7	5	6	12	8	2

Class Interval	20-29	30-39	40-49	50-59	60-69	70-79
Frequency	12	20	14	6	5	3

Class Interval	51-60	61-70	71-80	81-90	91-100	101-110
Frequency	4	10	15	20	15	4

Class Interval (Marks)	0-10	10-20	20-30	30-40	40-50
Number of Students	15	20	35	p	10

Size Number of Items	4–8	8–12	12–16	16–20	20–24	24–28	28–32
Frequency	9	10	18	14	10	6	3

Class	0–5	5–10	10–15	15–20	20–25	25–30	30–35
Frequency	5	12	18	28	17	12	8

Class	45–54	55–64	65–74	75–84	85–94	95–105
Frequency	8	13	19	32	12	6

Marks \((x_i)\)	0–4	5–9	10–14	15–19	20–24	25–29	30–34	35–39
Frequency \((f_i)\)	4	5	7	8	7	5	6	3

Value	Less than 10	Less than 20	Less than 30	Less than 40	Less than 50	Less than 60	Less than 70	Less than 80
Frequency	4	16	40	76	96	112	120	125

Class Interval	5-14	15-24	25-34
Frequency	3	6	18

35-44	45-54	55-64
Frequency	20	10	3

Class Interval	0-20	20-40	40-60	60-80	80-100
Frequency	7	11	K	9	13

30-40	40-50	50-60	60-70
15	10	8	5

Age (in years)	16–18	18–20	20–22	22–24	24–26
Number of Candidates	45	75	38	22	20