For the data 95 10 7 9 10 11 8 12 7 6 9, find the raw scores that correspond to the following : z= +1.22; z= -0.48
you have to find the mean and the standard deviation of the data.
mean = 16.7 sd =26.02 this is if the first number is 95, but I am thinking you meant 9 and 5.
mean =8.58
sd = 2.065
To find a z-score subtract the mean from the given value and divide by the sd.
To find the raw scores corresponding to specific z-scores, we need to use the formula:
X = (Z * SD) + mean
Where:
X = Raw score
Z = Z-score
SD = Standard deviation
mean = Mean
Given the data 95, 10, 7, 9, 10, 11, 8, 12, 7, 6, and 9, we can calculate the mean and standard deviation to find the desired raw scores.
Step 1: Calculate the mean (average) of the data:
mean = (95 + 10 + 7 + 9 + 10 + 11 + 8 + 12 + 7 + 6 + 9) / 11 = 11
Step 2: Calculate the standard deviation (SD):
To find the standard deviation, we first need to find the variance.
a. Calculate the deviation for each data point:
Deviation = Data point - mean
Deviation = 95 - 11 = 84
Deviation = 10 - 11 = -1
Deviation = 7 - 11 = -4
Deviation = 9 - 11 = -2
Deviation = 10 - 11 = -1
Deviation = 11 - 11 = 0
Deviation = 8 - 11 = -3
Deviation = 12 - 11 = 1
Deviation = 7 - 11 = -4
Deviation = 6 - 11 = -5
Deviation = 9 - 11 = -2
b. Calculate the squared deviation for each data point:
Squared Deviation = Deviation^2
Squared Deviation = 84^2 = 7056
Squared Deviation = (-1)^2 = 1
Squared Deviation = (-4)^2 = 16
Squared Deviation = (-2)^2 = 4
Squared Deviation = (-1)^2 = 1
Squared Deviation = 0^2 = 0
Squared Deviation = (-3)^2 = 9
Squared Deviation = 1^2 = 1
Squared Deviation = (-4)^2 = 16
Squared Deviation = (-5)^2 = 25
Squared Deviation = (-2)^2 = 4
c. Calculate the variance:
variance = (Sum of Squared Deviations) / (Number of data points)
variance = (7056 + 1 + 16 + 4 + 1 + 0 + 9 + 1 + 16 + 25 + 4) / 11
variance = 7137 / 11
variance = 648.82
d. Calculate the standard deviation (SD):
SD = √variance
SD = √648.82
SD = 25.47
Step 3: Find the raw scores.
a. For z = +1.22:
X = (Z * SD) + mean
X = (1.22 * 25.47) + 11
X = 31.07 + 11
X = 42.07
b. For z = -0.48:
X = (Z * SD) + mean
X = (-0.48 * 25.47) + 11
X = -12.22 + 11
X = -1.22
Therefore, the raw scores corresponding to z = +1.22 and z = -0.48 are 42.07 and -1.22, respectively.
To find the raw scores that correspond to specific z-scores, you can use the formula:
Raw Score = (Z-Score * Standard Deviation) + Mean
Given the data: 95 10 7 9 10 11 8 12 7 6 9
To find the raw score corresponding to z = +1.22, you need to know the mean and standard deviation. Let's assume the mean is μ = 10 and the standard deviation is σ = 2.
For z = +1.22:
Raw Score = (1.22 * 2) + 10
= 2.44 + 10
= 12.44
Therefore, the raw score that corresponds to z = +1.22 is 12.44.
Now, to find the raw score corresponding to z = -0.48:
Raw Score = (-0.48 * 2) + 10
= -0.96 + 10
= 9.04
Therefore, the raw score that corresponds to z = -0.48 is 9.04.
Note that the mean and standard deviation used in this calculation are assumed. If you have the actual mean and standard deviation for your dataset, you should use those values instead.