Advertisements
Advertisements
Question
If x is the mean of the ten natural numbers `x_1, x_2 , x_3+....... + x_10` show that (x1 -x) + (x2 - x) +.........+ (x10 - x)` = 0
Solution
We have , x = `( x_1 + x_2 +...... + x_10) / 10`
⇒ `x_1 +x_2 + ..........+ x_10 = 10barx ..... (1)`
⇒ Now , `(x_1 - barx) + (x_2- barx)+.........+ (x_10 - barx)`
⇒ `10barx - 10barx` [By equation (1)]
∴ `(x_2- barx) + (x_2 - barx) +.......+ (x_10 - barx)`0 Hence proved.
APPEARS IN
RELATED QUESTIONS
In a mathematics test given to 15 students, the following marks (out of 100) are recorded:-
41, 39, 48, 52, 46, 62, 54, 40, 96, 52, 98, 40, 42, 52, 60
Find the mean, median and mode of this data.
Find the mean salary of 60 workers of a factory from the following table:-
| Salary (in Rs) | Number of workers |
| 3000 | 16 |
| 4000 | 12 |
| 5000 | 10 |
| 6000 | 8 |
| 7000 | 6 |
| 8000 | 4 |
| 9000 | 3 |
| 10000 | 1 |
| Total | 60 |
Following are the weights (in kg) of 10 new born babies in a hospital on a particular day:
3.4, 3.6, 4.2, 4.5, 3.9, 4.1, 3.8, 4.5, 4.4, 3.6. Find the mean x.
The mean weight of 8 numbers is 15. If each number is multiplied by 2, what will be the new mean?
Find the values of n and X in each of the following cases :
(i) `sum _(i = 1)^n`(xi - 12) = - 10 `sum _(i = 1)^n`(xi - 3) = 62
(ii) `sum _(i = 1)^n` (xi - 10) = 30 `sum _(i = 6)^n` (xi - 6) = 150 .
Find the mean of the following distribution:
| x : | 10 | 12 | 20 | 25 | 35 |
| F : | 3 | 10 | 15 | 7 | 5 |
Find the median of the following data (1-8)
92, 35, 67, 85, 72, 81, 56, 51, 42, 69
If the difference of mode and median of a data is 24, then find the difference of median and mean.
Find the median of the observations, 59, 75, 68, 70, 74, 75, 80.
If the mean of the following data is 20.2, then find the value of p.
| xi | 10 | 15 | 20 | 25 | 30 |
| fi | 6 | 8 | p | 10 | 6 |
