Advertisements
Advertisements
Question
Find the mean of each of the following frequency distributions
| Class interval | 10 - 30 | 30 - 50 | 50 - 70 | 70 - 90 | 90 - 110 | 110 - 130 |
| Frequency | 5 | 8 | 12 | 20 | 3 | 2 |
Solution
Let the assume mean A = 60
| Class interval | Mid value(x1) | d1 = x1 - 60 | `"u"_1=(x_1-60)/20` | f1 | f1u1 |
| 10 - 30 | 20 | -40 | -2 | 5 | -10 |
| 30 - 50 | 40 | -20 | -1 | 8 | -8 |
| 50 - 70 | 60 | 0 | 0 | 12 | 0 |
| 70 - 90 | 80 | 20 | 1 | 20 | 20 |
| 90 -110 | 100 | 40 | 2 | 3 | 6 |
| 110 - 130 | 120 | 60 | 3 | 2 | 6 |
| N = 50 | `sumf_1"u"_1=14` |
We have
A = 60, h = 20
Mean `=A+hxx(sumf_1"u"_1)/N`
`=60+20xx14/50`
`=60+280/50`
= 60 + 5.6
= 65.6
RELATED QUESTIONS
The measurements (in mm) of the diameters of the head of the screws are given below:
| Diameter (in mm) | No. of Screws |
| 33 — 35 | 10 |
| 36 — 38 | 19 |
| 39 — 41 | 23 |
| 42 — 44 | 21 |
| 45 — 47 | 27 |
Calculate mean diameter of head of a screw by ‘Assumed Mean Method’.
Calculate the mean for the following distribution:-
| x | 5 | 6 | 7 | 8 | 9 |
| f | 4 | 8 | 14 | 11 | 3 |
The following table gives the number of children of 150 families in a village. Find the average number of children per family.
| No. of children (x) | 0 | 1 | 2 | 3 | 4 | 5 |
| No. of families (f) | 10 | 21 | 55 | 42 | 15 | 7 |
Find the mean of each of the following frequency distributions
| Class interval | 50 - 70 | 70 - 90 | 90 - 110 | 110 - 130 | 130 - 150 | 150 - 170 |
| Frequency | 18 | 12 | 13 | 27 | 8 | 22 |
Find the mean of each of the following frequency distributions
| Class interval | 0 - 8 | 8 - 16 | 16 - 24 | 24 - 32 | 32 - 40 |
| Frequency | 6 | 7 | 10 | 8 | 9 |
Find the mean of the following data, using step-deviation method:
| Class | 5 – 15 | 15-20 | 20-35 | 35-45 | 45-55 | 55-65 | 65-75 |
| Frequency | 6 | 10 | 16 | 15 | 24 | 8 | 7 |
Find the mean of the following distribution:
| x | 4 | 6 | 9 | 10 | 15 |
| f | 5 | 10 | 10 | 7 | 8 |
Consider the following distribution of SO2 concentration in the air (in ppm = parts per million) in 30 localities. Find the mean SO2 concentration using assumed mean method. Also find the values of A, B and C.
| Class interval | Frequency (fi) | Class mark (xi) | di = xi - a |
| 0.00 - 0.04 | 4 | 0.02 | -0.08 |
| 0.04 - 0.08 | 9 | 0.06 | A |
| 0.08 - 0.12 | 9 | 0.10 | B |
| 0.12 - 0.16 | 2 | 0.14 | 0.04 |
| 0.16 - 0.20 | 4 | 0.18 | C |
| 0.20 - 0.24 | 2 | 0.22 | 0.12 |
| Total | `sumf_i=30` |
In calculating the mean of grouped data, grouped in classes of equal width, we may use the formula `barx = a + (sumf_i d_i)/(sumf_i)` where a is the assumed mean. a must be one of the mid-points of the classes. Is the last statement correct? Justify your answer.
Find the mean of the following data using assumed mean method:
| Class | 0 – 5 | 5 – 10 | 10 – 15 | 15 – 20 | 20 – 25 |
| Frequency | 8 | 7 | 10 | 13 | 12 |
