Mean For A Group Frequency Distribution

Statistics of Class 10

Mean For A Group Frequency Distribution

DIRECT METHOD:

Step 1: For each class, find the class mark x_i as

x_i= 1/2 (lower limit + upper limit)

Step 2: Calculate f_ix_i for each i.

Step 3: Use the formula : Mean For A Group Frequency Distribution ;

question 1. Find the arithmetic mean of 1, 2, 3, …., n.

Solution: The arithmetic mean of 1, 2, 3, ….., n is given by

Mean For A Group Frequency Distribution

question 2. If the mean of n observations is Mean For A Group Frequency Distribution , then find the new mean when the first term is increased by 1, second term by 2, and so on.

Solution:

Mean For A Group Frequency Distribution

ASSUMED MEAN METHOD:

Following steps are taken to solve cases by assumed-mean method.

Step 1: For each class interval, calculate the class mark xi by using the

formula: x_i= 1/2 (lower limit + upper limit).

Step 2: Choose a value of xi in the middle as the assumed mean and denote it by A.

Step 3: Calculate the deviations d_{i =}(d_{_i}- A) for each i.

Step 4: Calculate the( f_id_i)for each i.

Step 5: Find n = Mean For A Group Frequency Distribution .

Step 6: Calculate the mean, Mean For A Group Frequency Distribution , by using the formula: .

question 1. Using the assumed-mean method, find the mean of the following data:

Class	0 – 10	10 – 20	20 – 30	30 – 40	40 – 50
Frequency	7	8	12	13	10

Solution: Let A = 25 be the assumed mean. Then, we have:

Class interval	Frequency fi	Midvalue xi	Deviation di = (xi – 25)	(fi di)
0 – 10	7	5	–20	–140
10 – 20	8	15	–10	–80
20 – 30	12	25 = A	0	0
30 – 40	13	35	10	130
40 – 500	10	45	20	200
			Σfi = 50	Σ(fi di)= 110

Mean For A Group Frequency Distribution .

Hence, mean = 27.2.

STEP-DEVIATION METHOD:

Following steps are taken to solve cases by step-deviation method.

Step 1: For each class interval, calculate the class mark xi by using the formula:

x_i= 1/2 (lower limit + upper limit).

Step 2: Choose a value of xi in the middle of the xi column as the assumed mean and denote it by A.

Step 3: Calculate h = [(upper limit) – (lower limit)].

Step 4: Calculate Mean For A Group Frequency Distribution for each class.

Step 5: Calculate fiui for each class and find Mean For A Group Frequency Distribution .

Step 6: Calculate the mean, by using the formula: Mean For A Group Frequency Distribution .

question 1. Calculate the mean of the following frequency distribution, using the step-deviation method:

Class interval	Frequency
0 – 50	17
50 – 100	35
100 – 150	43
150 – 200	40
200 – 250	21
250 – 300	24

Solution: Here, h = 50. Let the assumed mean be A = 125.

For calculating the mean, table is prepared as follows :

Class interval	Frequency fi	Midvalue xi		(fi ui)
0 – 50	17	25	–2	–34
50 – 100	35	75	–1	–35
100 – 150	43	125 = A	0	0
150 – 200	40	175	1	40
200 – 250	21	225	2	42
250 – 300	24	275	3	72
			Σfi = 180	Σ(fi ui)= (154–69) = 85

Thus, we have

A = 125, h = 50, Mean For A Group Frequency Distribution = 180 and = 85.

Mean, Mean For A Group Frequency Distribution

= 125 + [50 x 85/180]

= (125 + 23.61) = 148.61 .

Hence, the mean of the given frequency is 148.61.

MEAN FOR AN EXCLUSIVE SERIES:

question 1. Find the mean age (in years) from the following frequency distribution:

Age(in years)	15–19	20–24	25–29	30–34	35–39	40–44	45–49	Total
Frequency	3	13	21	15	5	4	2	63

Solution: The given series is an Inclusive series. Making it an exclusive

Age (in years)	Frequency fi	Midvalue xi	= (x_i - 32)/5	(fi ui)
14.5 – 19.5	3	17	–3	–9
19.5 – 24.5	13	22	–2	–26
24.5 – 29.5	21	27	–1	–21
29.5 – 34.5	15	32 = A	0	0
34.5 – 39.5	5	37	1	5
39.5 – 44.5	4	42	2	8
44.5 – 49.5	2	47	3	6
			Σfi = 63	Σ(fi ui)= (19–56) = –37