Can you step by srep dumb this down so that I can understand how to get the answer please?
A set of 50 data values has a mean of 15 and a variance of 36. Find the standard score of a data value = 21
Z = (score-mean)/SD
SD = √variance
Insert values and compute.
Sure! I can help break it down step by step for you.
1. To find the standard score of a data value, also known as the z-score, we need to calculate how many standard deviations away that value is from the mean.
2. The formula for calculating the z-score is: z = (x - μ) / σ, where z is the standard score, x is the data value, μ is the mean, and σ is the standard deviation.
3. We already know the mean of the data set is 15.
4. To find the standard deviation, we need to take the square root of the variance. In this case, the variance is given as 36. So, the standard deviation is √36 = 6.
5. Now we can apply the formula to find the z-score of the data value 21.
z = (21 - 15) / 6 = 6 / 6 = 1.
6. So, the standard score (z-score) for the data value 21 is 1.
To summarize, to find the standard score of a data value:
- Subtract the mean from the data value.
- Divide the result by the standard deviation.
I hope this helps! Let me know if you have any further questions.