87,89,90,90,98,99,99,101,102,103,104
Within how many standard deviations of the mean is the value 102?
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 is your score in terms of standard deviations (SD).
Z = (score-mean)/SD
I'll let you do the calculations.
To determine the number of standard deviations away from the mean a value is, we need to calculate the mean and standard deviation of the data set. Since you have provided the data set, we can use that.
Step 1: Calculate the Mean
To find the mean, add up all the values in the data set and divide by the total number of values.
mean = (87 + 89 + 90 + 90 + 98 + 99 + 99 + 101 + 102 + 103 + 104) / 11
= 1092 / 11
≈ 99.27
Step 2: Calculate the Standard Deviation
To find the standard deviation, we need to calculate the variance first. Then, taking the square root of the variance gives us the standard deviation.
variance = [(87 - mean)^2 + (89 - mean)^2 + ... + (104 - mean)^2] / (n - 1)
standard deviation = sqrt(variance)
Here's a step-by-step calculation of the variance:
tempSum = (87 - 99.27)^2 + (89 - 99.27)^2 + ... + (104 - 99.27)^2
variance = tempSum / (11 - 1)
To calculate the standard deviation, take the square root of the variance.
Once you have calculated the standard deviation, you can determine how many standard deviations away from the mean the value 102 is by using the formula:
z-score = (value - mean) / standard deviation
In this case:
z-score = (102 - mean) / standard deviation
Now, you can plug in the mean and standard deviation values to calculate the z-score and determine how many standard deviations away from the mean the value 102 is.