Question

the standard deviation of 10 value is 3. if each value is increased by 4. find their the variance of new set of value​

Answer 1

Answer:

No change in variance if each number increase by 4.

So variance = Square(SD) = 3*3 = 9.

Step-by-step explanation:

Standard Deviation of 10 values = 3 = SD

SD is square root of average of variance square.

Given in equation form as

SD = √(variance)

Variance = sum of square of difference of each number from mean divided by total number.

Variance = ∑(xi - mean)²/N

xi = Each term

Mean = Average of all numbers

N - Number of terms.

When the original numbers increased by 4, the total numbers remain same.

Hence N is no change.

xi will increase by 4, mean also increase by 4.

So xi - mean remain same.

Hence no change in variance.

So variance = Square(SD) = 3*3 = 9.

Answer 2

Question :- The standard deviation of 10 values is 3. if each value is increased by 4, then find the variance of the new set of values ?

Solution :-

we know that,

• If we add same constant value let k in median, mean, and quartiles , they will be changed by adding constant(k) to each value.
• However, the range, interquartile range, standard deviation and variance will remain the same.

• if we Multiplying every value by a constant(k), we also have to multiply the mean, median, quartiles, range, interquartile range, and standard deviation by that constant(k), and multiply the variance (which is simply the square of the standard deviation) by the square of that constant(k).

given that,

→ old standard deviation of 10 values = 3

→ constant number is added in each value = k = 4 .

therefore,

→ New standard deviation of new 10 values = old standard deviation of 10 values = 3 .

hence,

→ New variance = (New standard deviation)² = (3)² = 9 (Ans.)

Learn more :-

calculate the median and mode from the following income between (rs)100-200 100-300 100-400 100-500 100-600 no of person...

https://brainly.in/question/23585381

Some students of class X donated for the welfare of old age persons. The contributions are shown in the following distri...

https://brainly.in/question/17314012