Do these sample FICO scores appear to be consistent with the reported mean? 714 751 664 789 818 779 698 836 753 834 693 802
To determine whether these sample FICO scores appear to be consistent with the reported mean, we first need to calculate the mean of the sample scores.
To calculate the mean, add up all the scores and divide by the total number of scores.
Sum of all the scores: 714 + 751 + 664 + 789 + 818 + 779 + 698 + 836 + 753 + 834 + 693 + 802 = 9481
Total number of scores: 12
Mean = Sum of scores / Total number of scores = 9481 / 12 = 790.08 (rounded to two decimal places)
The reported mean is not given, so we cannot directly compare it with the calculated mean. However, if we assume that the reported mean is 790, we can make a comparison.
Comparing the calculated mean (790.08) with the assumed reported mean (790), we can see that the sample scores are relatively close to the mean. However, to make a more accurate determination, we need to consider the dispersion (spread) of the sample scores.
To assess the consistency of the sample scores with the mean, we can calculate the standard deviation. The standard deviation measures the average amount by which the scores differ from the mean.
Using a statistical calculator or software, calculate the standard deviation of the sample scores.
For these scores: 714, 751, 664, 789, 818, 779, 698, 836, 753, 834, 693, 802;
we find that the standard deviation is approximately 57.09 (rounded to two decimal places).
Now, we can compare the mean and the standard deviation. If the standard deviation is relatively small compared to the mean, it suggests that the scores are more consistent with the mean. However, if the standard deviation is relatively large compared to the mean, it suggests that the scores are more spread out and less consistent with the mean.
In this case, the standard deviation (57.09) is relatively small compared to the mean (790.08), indicating that the scores are relatively consistent with the mean.
However, keep in mind that this analysis assumes an assumed reported mean of 790. If the actual reported mean is different, the comparison may change.