Advertisements
Advertisements
प्रश्न
The mean of n observations is X. If k is added to each observation, then the new mean is
पर्याय
X
X + k
X − k
kX
उत्तर
Let us take n observations X1.,....,Xn.
If `bar(X) `be the mean of the n observations, then we have
`bar(X) = 1/n sum_(i=1)^n X_i`
`⇒ sum_(i=1)^nX_i = nbar(X)`
Add a constant k to each of the observations. Then the observations becomes `X_i+k,...,X_n+k`
If `bar(Y) `be the mean of the new observations, then we have
`bar(Y) = 1/n sum_(i=1)^n(X_i+k)`
=`1/nsum _(i=1)^n X_i + 1/n sum_(i=1) ^n k `
`= bar(X) +1/n. nk `
`= bar(X) + k `
Hence, the correct choice is (b).
APPEARS IN
संबंधित प्रश्न
Give one example of a situation in which
(i) the mean is an appropriate measure of central tendency.
(ii) the mean is not an appropriate measure of central tendency but the median is an appropriate measure of central tendency.
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 |
The mean weight per student in a group of 7 students is 55 kg. The individual weights of 6
of them (in kg) are 52, 54, 55, 53, 56 and 54. Find the weight of the seventh student.
The mean weight of 8 numbers is 15. If each number is multiplied by 2, what will be the new mean?
Calculate the mean for the following distribution:
| x : | 5 | 6 | 7 | 8 | 9 |
| f : | 4 | 8 | 14 | 11 | 3 |
Find the mean of the following distribution:
| x : | 10 | 12 | 20 | 25 | 35 |
| F : | 3 | 10 | 15 | 7 | 5 |
Numbers 50, 42, 35, 2x + 10, 2x − 8, 12, 11, 8 are written in descending order and their
median is 25, find x.
If the median of scores \[\frac{x}{2}, \frac{x}{3}, \frac{x}{4}, \frac{x}{5}\] and \[\frac{x}{6}\] (where x > 0) is 6, then find the value of \[\frac{x}{6}\] .
In a frequency distribution, the mid-value of a class is 10 and the width of the class is 6. The lower limit of the class is ______.
A child says that the median of 3, 14, 18, 20, 5 is 18. What doesn’t the child understand about finding the median?
