given the following population data, x=17,13,23,15,19,19,21,28 calculate the z score value for a score of 18.

Find the mean first = sum of scores/number of scores

Subtract each of the scores from the mean and square each difference. Find the sum of these squares. Divide that by the number of scores to get variance.

Standard deviation = square root of variance

Z = (score-mean)/SD

I'll let you do the calculations.

To calculate the z-score value for a score of 18, you need to follow these steps:

Step 1: Calculate the mean (average) of the given population data.
To find the mean, sum all the values and divide by the total number of data points.

x = 17, 13, 23, 15, 19, 19, 21, 28
Mean = (17 + 13 + 23 + 15 + 19 + 19 + 21 + 28) / 8
Mean = 155 / 8
Mean = 19.375

Step 2: Calculate the standard deviation of the population data.
The standard deviation quantifies the amount of variation or dispersion in the data set.

To calculate the standard deviation, you need to calculate the variance first. Variance is the average of the squared differences from the mean.

Variance = (|17 - 19.375|^2 + |13 - 19.375|^2 + |23 - 19.375|^2 + |15 - 19.375|^2 + |19 - 19.375|^2 + |19 - 19.375|^2 + |21 - 19.375|^2 + |28 - 19.375|^2) / 8

Variance = (6.015625 + 48.515625 + 13.515625 + 20.015625 + 0.140625 + 0.140625 + 0.265625 + 67.015625) / 8
Variance = 155.625 / 8
Variance = 19.453125

Standard Deviation = √Variance
Standard Deviation ≈ √19.453125
Standard Deviation ≈ 4.406

Step 3: Calculate the z-score.
The z-score measures how many standard deviations a score is from the mean.

Z-Score = (18 - Mean) / Standard Deviation
Z-Score = (18 - 19.375) / 4.406
Z-Score ≈ -0.311

Therefore, the z-score value for a score of 18 is approximately -0.311.