Question: Between test 1 (score of 230 and mean of 210 and standard deviation of 22) and test 2 (score of 80 and mean of 70 and standard deviation of 8), which one is better? Explain your reasoning.
I know that test 2 is better. I am not good at giving the reasoning but I think that it is due to how closer the score is to the mean.
what do you mean by "better"? Closer to the mean?
Farther above the mean -- more std away?
In any case, check the number of std from the mean; that's probably the first step.
Nevermind it is test 2.
Test 1= z220=220-200/21=20/21=0.95=.33
Test 2= z90=90-80/8=10/8=1.25=.40
your : Test 1= z220=220-200/21=20/21=0.95=.33
doesn't even match the data given in the question.
prob(x < 230)
z-score = (230 - 210)/22 = .9091
your ... = 0.95 = .33 makes no sense
To determine which test is better, we need to consider both the score and the associated mean and standard deviation. Here's how you can reason through it:
1. Calculate the z-scores: Start by calculating the z-scores for both test scores. The z-score measures how many standard deviations a particular score is away from the mean. The formula to calculate the z-score is: Z = (X - mean) / standard deviation.
For Test 1:
Z1 = (230 - 210) / 22
Z1 ≈ 0.91
For Test 2:
Z2 = (80 - 70) / 8
Z2 ≈ 1.25
2. Interpret the z-scores: Now, interpret the z-scores you calculated. A positive z-score indicates that the score is above the mean, while a negative z-score indicates a score below the mean. The magnitude of the z-score indicates how far the score deviates from the mean in terms of standard deviations.
In this case, both Test 1 and Test 2 have positive z-scores, which means both scores are above their respective means. However, Test 2 has a higher magnitude z-score, suggesting that the score is further above its mean compared to Test 1.
3. Consider the distance from the mean: The magnitude of the z-score also reflects how far the score is from the mean. A higher magnitude z-score indicates a greater distance from the mean.
In this case, Test 2 has a higher magnitude z-score (1.25) compared to Test 1 (0.91). This suggests that Test 2's score is further away from its mean compared to Test 1's score.
4. Analyze relative to standard deviation: Additionally, consider the standard deviation. A smaller standard deviation generally indicates less variability in the data.
In this case, Test 2 has a smaller standard deviation (8) compared to Test 1 (22). This indicates that Test 2's scores have less variability, which may imply greater consistency or reliability.
Considering all these factors, Test 2 is indeed better than Test 1. The score of Test 2 is further above its mean and has less variability compared to Test 1, suggesting better performance in relation to the class or population.