Question

She doesn't remember the mean or the standard deviation, but she does remember that the first and third quartiles are 500 and 600. The standard deviation of SAT Verbal scores is closest to

Answer 1

the standard deviation is approx 74.07 which closest to 75

Explanation:

The standard deviation can be estimated with the formula below provided the sample does not deviate from normal distribution

S.D approx = q₃ - q₁ / 1.35 where q₃ = 600, and q₁ = 500

S.D approx = 100 / 1.35 = 74.07

Answer 2

The standard deviation of SAT Verbal scores is 74.07 which is closest to 75

Explanation:

Given that:

`Q_(1)=500\\\\Q_(3)=600\\`

Using quartile equations:

`Q_(1)\approx \mu-(0.675)\sigma = 500---(1)\\\\Q_(#)\approx \mu+(0.675)\sigma = 600---(2)\\`

Adding (1) and (2)

`2\mu =1100\\\\\mu=550`

Inserting in (1) or (2)

`550-(0.675)\sigma=500\\\\\sigma=(-50)/(-0.675)\\\\\sigma=74.07\\\\Or \,\,from\,\,(2)\\\\550+(0.675)\sigma=600\\\\\sigma=(50)/(0.675)\\`