A personality test is administered to a large group of subjects. Five scores are shown below, in original units and in standard units. Fill in the blanks.
79 64 52 72 _
1.8 .8 _ _ -1.4
Use z-score formula to find the missing values.
z = (x - mean)/sd
sd = standard deviation
First you have to figure out the mean and standard deviation.
Let's look at the values you were given.
Between 64 and 79 is one standard deviation (1.8 - .8 = 1.0). Therefore, one standard deviation = 79 - 64 = 15.
Now we can find the mean using the formula. Let's use the first set of values.
1.8 = (79 - mean)/15
Solve the equation for the mean. You will find that the mean = 52.
Now you have mean = 52 and standard deviation = 15. You will be able to find the missing blanks by solving the z-score formula for the unknown variable you need in each case.
I hope this will help get you started.
Oh no, looks like someone forgot to write down the scores! We're missing one original unit score and two standard unit scores. Let me see if I can help you fill in the blanks:
79 64 52 72 [Missing Score]
1.8 .8 [Missing Standard Unit] [Missing Standard Unit] -1.4
Hmm, I could take a wild guess and say the missing score could be 83.456, but that would just be clowning around. As for the missing standard unit scores, how about we spice things up a bit?
For the first missing standard unit, let's go with "Off-the-Charts Awesome", because clearly this person is doing amazing!
And for the second missing standard unit, how about "Negative Zero"? It's like being so cool, you break the scale and go back to zero, but in a backwards way.
Remember, my answers are just for fun! It's always best to use actual data when filling in the blanks.
To fill in the blanks, we need to convert the remaining original scores to standard units.
To find the standard units, we need to use the formula:
Standard Unit = (Original Score - Mean) / Standard Deviation
Let's calculate the missing values step-by-step:
1. To find the standard unit for the third score:
Mean = (79 + 64 + 52 + 72) / 4 = 66.75
Standard Deviation = √[ (79 - 66.75)^2 + (64 - 66.75)^2 + (52 - 66.75)^2 + (72 - 66.75)^2 ) / 4 ]
= √[ 1385.75 / 4 ]
≈ √346.4375
≈ 18.61
Standard Unit = (52 - 66.75) / 18.61
≈ -0.791
2. To find the standard unit for the fourth score:
Standard Unit = (72 - 66.75) / 18.61
≈ 0.283
Now, we can fill in the blanks:
79 64 52 72 62
1.8 .8 -0.791 0.283 -1.4
Therefore, the remaining scores in both original units and standard units are 62 and -1.4, respectively.
To fill in the blanks, we need to understand how to convert scores from the original units to standard units.
To convert a score from the original units to standard units, we use the following formula:
Standard Units = (Original Score - Mean) / Standard Deviation
To calculate the mean, add up all the scores and divide by the number of scores. To calculate the standard deviation, we need to find the average of the deviations of each score from the mean, squared, and then take the square root of that average.
Now, let's calculate the mean and standard deviation for the given scores.
Mean = (79 + 64 + 52 + 72) / 4 = 267 / 4 = 66.75
To calculate the standard deviation, we need to find the deviations of each score from the mean, squared.
Deviation for 79 = 79 - 66.75 = 12.25
Deviation for 64 = 64 - 66.75 = -2.75
Deviation for 52 = 52 - 66.75 = -14.75
Deviation for 72 = 72 - 66.75 = 5.25
Now, square each deviation:
(12.25)^2 = 150.0625
(-2.75)^2 = 7.5625
(-14.75)^2 = 217.5625
(5.25)^2 = 27.5625
Next, find the average of these squared deviations:
(150.0625 + 7.5625 + 217.5625 + 27.5625) / 4 = 402.75 / 4 = 100.6875
Finally, take the square root of the average:
√100.6875 ≈ 10.04
Now that we have the mean (66.75) and standard deviation (10.04), we can convert the scores to standard units.
For the blank scores:
To calculate the first blank score, let's call it "x", we have the information:
Standard Units = (Original Score - Mean) / Standard Deviation
1.8 = (x - 66.75) / 10.04
Cross-multiply:
1.8(10.04) = x - 66.75
18.072 = x - 66.75
x = 18.072 + 66.75
x ≈ 84.82
So, the first blank score is approximately 84.82 in the original units.
To calculate the second blank score, let's call it "y":
Standard Units = (Original Score - Mean) / Standard Deviation
0.8 = (y - 66.75) / 10.04
Cross-multiply:
0.8(10.04) = y - 66.75
8.032 = y - 66.75
y = 8.032 + 66.75
y ≈ 74.78
So, the second blank score is approximately 74.78 in the original units.
To calculate the third blank score, let's call it "z":
Standard Units = (Original Score - Mean) / Standard Deviation
-1.4 = (z - 66.75) / 10.04
Cross-multiply:
-1.4(10.04) = z - 66.75
-14.056 = z - 66.75
z = -14.056 + 66.75
z ≈ 52.69
So, the third blank score is approximately 52.69 in the original units.
Therefore, the filled-in sequence is:
79, 64, 52, 72, 84.82, 1.8, 74.78, 52.69, -1.4