If the mean and median of a statistical distribution are 35 and 33, respectively, determine the mode of the distribution.

Q.If the mean and median of a statistical distribution are 35 and 33, respectively, determine the mode of the distribution.

\(2\times\) Mean = \(3\times\) Median - Mode
Or, \(2\times 35 = 3\times 33\) - Mode
Or, Mode \(= 3\times 33 - 2\times 35\)
\(= 99 - 70 = 29\)

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	0-5	5-10	10-15
Frequency	5	12	18

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

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

Age (in years)	30–34	35–39	40–44	45–49	50–54	55–59
Number of Individuals	10	12	15	6	4	3

Weight (kg)	Less than 38	Less than 40	Less than 42
Number of Students	0	4	6

Less than 44	Less than 46	Less than 48	Less than 50	Less than 52
9	12	28	32	35