Compute the mode from the following data:

Class
interval 1-5 6-10 11-15 16-20 21-25 26-30 31-35 36-40 41-45 46-50

Frequency 3 8 13 18 28 20 13 8 6 4

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Solution

Clearly, we have to find the mode of the data. The given data is an inclusive series. So, we will convert it to an exclusive form as given below:

Class interval 0.5-5.5 5.5-10.5 10.5-15.5 15.5-20.5 20.5-25.5 25.5-30.5 30.5-35.5 35.5-40.5 40.5-45.5 45.5-50.5

Frequency 3 8 13 18 28 20 13 8 6 4

As the class 20.5-25.5 has the maximum frequency, it is the modal class.

$Now, x_{k} = 20.5, h = 5, f_{k} = 28, f_{k - 1} = 18 and f_{k + 1} = 20 ∴ Mode, M_{0} = x_{k} + \{h \times \frac{(f_{k} - f_{k - 1})}{(2 f_{k} - f_{k - 1} - f_{k + 1})}\} = 20.5 + \{5 \times \frac{(28 - 18)}{(2 \times 28 - 18 - 20)}\} = 20.5 + \{5 \times \frac{10}{18}\} = (20.5 + 2.78) = 23.28$

Hence, mode=23.28

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Class	1-5	6-10	11-15	16-20	21-25	26-30	31-35	35-40	41-45
Frequency	7	10	16	32	24	16	11	5	2

Class-Interval	0−5	5−10	10−15	15−20	20−25	25−30	30−35	35−40
Frequency	5	7	15	18	16	9	6	3

Age (in years)	0-5	5-10	10-15	15-20	20-25	25-30	30-35
Number of patients	6	11	18	24	17	13	5

Class Interval	1−5	6−10	11−15	16−20	21−25	26−30	31−35
Frequency	2	8	15	35	20	10	14

Find the median of the following data:

Class interval	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	Total
Frequency	$8$	$16$	$36$	$34$	$6$	$100$

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Class interval	1-5	6-10	11-15	16-20	21-25	26-30	31-35	36-40	41-45	46-50
Frequency	3	8	13	18	28	20	13	8	6	4

Class interval	0.5-5.5	5.5-10.5	10.5-15.5	15.5-20.5	20.5-25.5	25.5-30.5	30.5-35.5	35.5-40.5	40.5-45.5	45.5-50.5
Frequency	3	8	13	18	28	20	13	8	6	4