Henry's z-score on his reading test was 1.27. The class average was 60, the median was 58.5 and the variance was 6.2. What was Henry's "raw" score

(his score before converting to z-scores)

Z = (raw score - mean)/Standard deviation

Standard deviation = square root of variance

I hope this helps. Thanks for asking.

To find Henry's "raw" score, we need to use the formula for z-score:

z = (x - μ) / σ

where
z = z-score,
x = raw score,
μ = population mean,
σ = standard deviation.

In this case, we are given the z-score, the class average (μ), the median, and the variance (σ^2). Since variance is the square of the standard deviation, we need to take the square root of the variance to find the standard deviation:

σ = √6.2

Now, let's rearrange the formula to solve for x:

x = (z * σ) + μ

Plugging in the values:

σ = √6.2 ≈ 2.49
μ = class average = 60
z = 1.27

x = (1.27 * 2.49) + 60

Calculating:

x ≈ 3.17 + 60

x ≈ 63.17

Therefore, Henry's "raw" score (his score before converting to z-scores) was approximately 63.17.