Question

Standard deviation of four consecutive numbers in AP is 5. Then the common dofference in the series is

Answer 1

Answer:

Your answer if 2√5.

Hope this helps.

Step-by-step explanation:

Let d be the common difference and let a be the first of the four numbers

• Then the four numbers are:  a, a+d, a+2d, a+3d.
• The mean is half way between a+d and a+2d, so is:  a + 3d/2
• The deviations of each of the four numbers from the mean are:

a - ( a + 3d/2 ) = -3d/2

( a + d ) - ( a + 3d/2 ) = -d/2

( a + 2d ) - ( a + 3d/2 ) = d/2

( a + 3d ) - ( a + 3d/2 ) = 3d/2

• The sum of the squares of the deviations is then:

(-3d/2)² + (-d/2)² + (d/2)² + (3d/2)² = 9d²/4 + d²/4 + d²/4 + 9d²/4 = 20d²/4 = 5d²

• The variance is this divided by the number of terms:

variance = 5d²/4

• The standard deviation is the square root of this:

std dev = √5 d / 2

We are told this is 5, so

√5 d / 2 = 5  =>  d = 2√5