Class - Intervals
When the raw data are presented in a frequency distribution with equal or unequal, inclusive or exclusive class-intervals,we assume that, all the values falling into a particular class-interval are considered to be located at the mid point (called class-mark) of a class interval. The mid-points of the class interval is obtained by calculating the mean of the lower and the upper limits of the intervals.
Mid-point (mid-value) =Â
(or)
Mid-value = lower limit + [size of the class-interval]
Â
Calculate the mean of the following frequency distribution.
Class Interval |
Frequency |
0 - 8 | 6 |
8 - 16 | 7 |
16 - 24 | 10 |
24 - 32 | 8 |
32 - 40 | 9 Â |
Â
Mid-value=Â
Class- Interval | Mid-ValueÂ x_{i} | FrequencyÂ f_{i} | ProductÂ ofÂ x_{i}Â andÂ f_{iÂ Â Â Â } f_{i}x_{i} |
0 - 8 | 4 | 6 | 24 |
8 - 16 | 12 | 7 | 84 |
16 - 24 | 20 | 10 | 200 |
24 - 32 | 28 | 8 | 224 |
32 - 40 | 36 | 9 | 324 |
Total | Â | N =Â Î£f_{i}Â =Â 40 | Î£f_{i}x_{iÂ }= 856 |
HereÂ Î£f_{i}Â =40 andÂ Î£f_{i}x_{i}Â = 856
_{}
Mean = 21.4.
Â
Â Calculate the mean of the following frequency distribution.
Marks | No. of students | Marks | No. of students |
10 - 20 | 6 | 50 - 60 | 3 |
20 - 30 | 8 | 60 - 70 | 2 |
30 - 40 | 13 | 70 - 80 | 1 |
40 - 50 | 7 | Â | Â |
Â
Marks | Mid-valueÂ x_{i} |
No. of studentsÂ f_{i} |
f_{i}Â x_{i} |
10 - 20 | 15 | 6 | 90 |
20 - 30 | 25 | 8 | 200 |
30 - 40 | 35 | 13 | 455 |
40 - 50 | 45 | 7 | 315 |
50 - 60 | 55 | 3 | 165 |
60 - 70 | 65 | 2 | 130 |
70 - 80 | 75 | 1 | 75 |
Total | Â | N =Â Î£f_{i}Â = 40 | Î£f_{i}x_{iÂ }= 1430 |
=Â Â = 35.75
Mean = 35.75.
Â
Â
The expenditure (in Rs.) on water consumption of 52 houses in a locality is given in the table.
Expenditure in Rs. | 20 - 25 | 25 - 30 | 30 - 35 | 35 - 40 | 40 - 45 | 45 - 50 | 550 - 55 |
No. ofÂ Â Â Houses | 12 | 10 | 8 | 9 | 6 | 5 | 2 |
Find the average expenditure per house.
Arranging the distribution
Expenditure in Rs. | Class-MarkÂ Â x_{i} |
No. of housesÂ f_{i} |
f_{iÂ }x_{i} |
20 - 25 | 22.5 | 12 | 270 |
25 - 30 | 27.5 | 10 | 275 |
30 - 35 | 32.5 | 8 | 260 |
35 - 40 | 37.5 | 9 | 337.5 |
40 - 45 | 42.5 | 6 | 255 |
45 - 50 | 47.5 | 5 | 237.5 |
50 - 55 | 52.5 | 2 | 105 |
Total | Â | N =Â Î£f_{i}Â = 52 | Î£f_{i}x_{iÂ }= 1740 |
âˆ´Average expenditure per house on water =Â Â = Rs.Â Â = Rs. 33.46.
Â
Â Find the mean of the following frequency distribution.
Class Interval | 63 - 65 | 66 - 68 | 69 - 71 | 72 - 74 | 75 - 77 |
Frequency | 4 | 3 | 7 | 8 | 3 Â |
Class- IntervalÂ |
Mid-ValueÂ |
Frequency |
Â x_{i}Â f_{i} |
63 - 65 | 64 | 4 | 256 |
66 - 68 | 67 | 3 | 201 |
69 - 71 | 70 | 7 | 490 |
72 - 74 | 73 | 8 | 584 |
75 - 77 | 76 | 3 | 228 |
Total | Â | N =Â Î£f_{i}Â = 25 | Î£f_{i}x_{iÂ }= 1759 |
âˆ´Â MeanÂ Â =Â Â = 70.36.