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प्रश्न
Marks obtained by 40 students in a short assessment is given below, where a and b are two missing data.
| Marks | 5 | 6 | 7 | 8 | 9 |
| Number of Students | 6 | a | 16 | 13 | b |
If the mean of the distribution is 7.2, find a and b.
उत्तर १
| Marks (x) | Number of students (f) | fx |
| 5 | 6 | 30 |
| 6 | a | 6a |
| 7 | 16 | 112 |
| 8 | 13 | 104 |
| 9 | b | 9b |
| `sumf = 35 + a + b` | `sumfx = 246 + 6a + 9b` |
It is given that the number of students is 40.
∴ 35 + a + b = 40
`=>` a + b – 5 = 0 ...(1)
Mean = `(sumfx)/(sumf)`
`=> (246 + 6a + 9b)/(35 + a + b) = 7.2`
`=>` 246 + 6a + 9b = 7.2(35 + a + b)
`=>` 246 + 6a + 9b = 252 + 7.2a + 7.2b
`=>` 0 = 252 – 246 + 7.2a – 6a + 7.2b – 9b
`=>` 6 + 1.2a – 1.8b = 0
`=>` 10 + 2a – 3b = 0 ...(2)
Solving equations (1) and (2), we have
5a – 5 = 0
`=>` a = 1
From (1), we have b = 4
Hence, the values of a and b are 1 and 4 respectively.
उत्तर २
Mean = `(sumfx)/(sumf)`
`=> 7.2 = (6 xx 5 + a xx 6 + 16 xx 7 + 13 xx 8 + b xx 9)/(6 + a + 16 + 13 + b)`
`=> 7.2 = (246 + 6a + 9b)/(35 + a + b)`
`=>` 1.2 – 1.8b = –6 ...(i)
Total number of students = 6 + a + 16 + 13 + b
`=>` 40 = 35 + a + b
`=>` a + b = 5 ...(ii)
Multiple equation (ii) by 1.8 and add it to equation (i)
1.8a + 1.8b = 9
1.2a – 1.8b = –6
3a = 3
`=>` a = 1
Substituting = 1 in equation (ii) we get,
1 + b = 5
`=>` b = 4
उत्तर ३
| Marks (x) | No. of Students (f) | fx |
| 5 | 6 | 30 |
| 6 | a | 6a |
| 7 | 16 | 112 |
| 8 | 13 | 104 |
| 9 | b | 9b |
| Total | `sumf = 35 + a + b` | `sumfx = 246 + 6a + 9b` |
Now, `sumf` = 40
35 + a + b = 40
a + b = 5 ...(1)
And `barX = (sumfx)/(sumf)`
`7.2 = (246 + 6a + 9b)/(40)`
`=>` 6a + 9b + 246 = 288
`=>` 6a + 9b = 42
`=>` 2a + 3b = 14 ...(2)
From (1) and (2),
a = 1, b = 4
संबंधित प्रश्न
The ages of 40 students are given in the following table :
| Age (in years) | 12 | 13 | 14 | 15 | 16 | 17 | 18 |
| Frequency | 2 | 4 | 6 | 9 | 8 | 7 | 4 |
Find the arithmetic mean.
Find the mean (correct to one place of decimal) by using short-cut method.
|
x |
40 |
41 |
43 |
45 |
46 |
49 |
50 |
|
f |
14 |
28 |
38 |
50 |
40 |
20 |
10 |
Find the mode of the following:
21, 22, 28, 23, 24, 21 26, 22, 29, 27, 21, 21, 26, 24, 23
Find the median of the following:
25, 34, 31, 23, 22, 26, 35, 29, 20, 32
The mean of a certain number of observations is 32. Find the resulting mean, if the observation is, increased by 60%.
Find the mean of first five prime numbers.
Find the mean of: first five odd natural numbers
Find the median of the data: 24, 36, 46, 17, 18, 25, 35
A researcher studying the behavior of mice has recorded the time (in seconds) taken by each mouse to locate its food by considering 13 different mice as 31, 33, 63, 33, 28, 29, 33, 27, 27, 34, 35, 28, 32. Find the median time that mice spent in searching its food.
Find the median of the 10 observations 36, 33, 45, 28, 39, 45, 54, 23, 56, 25. If another observation 35 is added to the above data, what would be the new median?
