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Class 10 Class 12

Thirty women were examined in a hospital by a doctor and the number of heart beats per minute were recorded and summarised as follows. Find the mean heart beats per minute for these women, choosing a suitable method.

Number of heart beats per minute	65-68	68-71	71-74	74-77	77-80	80-83	83-86
Number of women	2	4	3	8	7	4	2

Here, we have

sum from blank to blank of straight f equals space 30 comma space space sum from blank to blank of straight f subscript straight i straight u subscript straight i equals 4 comma space

A (assumed mean) = 75.5 and h =3
Now,

top enclose straight x space equals space A plus fraction numerator begin display style sum from blank to blank of end style f subscript i u subscript i over denominator begin display style sum from blank to blank of end style f subscript i end fraction x h equals 75.5 plus 4 over 30 x 3 equals 75.5 plus 4 over 10 equals 75.5 plus 0.4 equals 75.9

Hence, the mean heart beats per minute is 75.9.

681 Views

Consider the following distribution of daily wages of 50 workers of a factory:

Daily wages (in Rs.)	Number of workers
100-120	12
120-140	14
140-160	8
160-180	6
180-200	10

Find the mean daily wages of the workers of the factory by using an appropriate method.

Hence, the mean daily wages of the workers of the factory is Rs. 145.20.

990 Views

The following distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is Rs. 18. Find the missing frequency 'f'.

Daily pocket allowance (in Rs.)	11-13	13-15	15-17	17-19	19-21	21-23	23-25
No. of childrens	7	6	9	13	f	5	4

Daily pocket allowance C.l.	No of children (f_i)	Mid-value x_i	f_ix_i
11-13	7	12	84
13-15	6	14	84
15-17	9	16	144
17-19	13	18	234
19-21	f	20	20f
21-23	5	22	110
23-25	4	24	96
	Σf_i = 44 + f		Σf_ix_i = 752 + 20f

Here, we have

top enclose x space equals space 18 comma space sum from blank to blank of f subscript i equals 44 plus f space a n d space sum from blank to blank of f subscript i x subscript i equals 752 space plus space 20 f

We know,

top enclose straight x space equals space fraction numerator begin display style sum from blank to blank of end style straight f subscript straight i straight x subscript straight i over denominator begin display style stack sum straight f subscript straight i with blank below and blank on top end style end fraction

rightwards double arrow

18 space equals space fraction numerator 752 plus 20 straight f over denominator 44 plus straight f end fraction

rightwards double arrow

18 (44 + f) = 752 + 20f

rightwards double arrow

792 + 18f = 752 + 20f

rightwards double arrow

18f - 20f = 752 - 792

rightwards double arrow

-2f = -40

rightwards double arrow

f = 20
Hence the Missing frequency is 20.

1158 Views

In a retail market, fruit venders were selling mangoes kept in packing boxes. These boxes contained varying number of mangoes. The following was the distribution of mangoes according to the number of boxes. Find the mean number of mangoes kept in a packing box. Which method of finding the mean did you choose?

No. of Mangoes	50-52	53-55	56-58	59-61	62-64
No. of boxes	15	110	135	115	25

Here
We have,

HereWe have,             Now,

Now,

top enclose straight x space equals space A plus fraction numerator begin display style sum from blank to blank of end style f subscript i u subscript i over denominator begin display style sum from blank to blank of end style f subscript i end fraction x space h equals 57 plus fraction numerator 37.50 over denominator 400 end fraction x 2 equals 57 plus fraction numerator 37.50 over denominator 200 end fraction

= 57 + 0.1875 = 57.1875

625 Views

A survey was conducted by a group of students as a part of their environment awareness programme, in which they collected the following data regarding the number of plants in 20 houses in a locality. Find the mean number of plants per house.

Number of plants

Number of houses

0-2

1

2-4

2

4-6

1

6-8

5

8-10

6

10-12

2

12-14

3

Which method did you use for finding the mean and why?

Number of plants	Number of houses (f_i)	Class mark (x_i)	f_ix_i
0-2	1	1	1
2-4	2	3	6
4-6	1	5	5
6-8	5	7	35
8-10	6	9	54
10-12	2	11	22
12-14	3	13	39
Total	Σf_i = 20		Σf_ix_i = 162

Here, we have

sum from blank to blank of straight f subscript straight i equals 20 comma space sum from blank to blank of straight f subscript straight i straight x subscript straight i

= 162

Now,

top enclose straight x equals fraction numerator begin display style sum from blank to blank of end style f subscript i x subscript i over denominator begin display style sum from blank to blank of end style f subscript i end fraction equals 162 over 2 equals 8.1

Hence, the mean number of plants per house = 8.1
We have used the direct method for finding the mean because numerical values of x_iand f_i are small.

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Statistics

Number of plants	Number of houses
0-2	1
2-4	2
4-6	1
6-8	5
8-10	6
10-12	2
12-14	3