Score Percentile Score Percentile Score Percentile Score Percentile
-3.5 0.02 -1 15.87 0 50 1.1 86.43
-3 0.13 -0.95 17.11 0.05 51.99 1.2 88.49
-2.9 0.19 -0.9 18.41 0.1 53.98 1.3 90.32
-2.8 0.26 -0.85 19.77 0.15 55.96 1.4 91.92
-2.7 0.35 -0.8 21.19 0.2 57.93 1.5 93.32
-2.6 0.47 -0.75 22.66 0.25 59.87 1.6 94.52
-2.5 0.62 -0.7 24.2 0.3 61.79 1.7 95.54
-2.4 0.82 -0.65 25.78 0.35 63.68 1.8 96.41
-2.3 1.07 -0.6 27.43 0.4 65.54 1.9 97.13
-2.2 1.39 -0.55 29.12 0.45 67.36 2 97.72
-2.1 1.79 -0.5 30.85 0.5 69.15 2.1 98.21
-2 2.28 -0.5 32.64 0.55 70.88 2.2 98.61
-1.9 2.87 -0.45 34.46 0.6 72.57 2.3 98.93
-1.8 3.59 -0.4 36.32 0.65 74.22 2.4 99.18
-1.7 4.46 -0.35 38.21 0.7 75.8 2.5 99.38
-1.6 5.48 -0.3 40.13 0.75 77.34 2.6 99.53
-1.5 6.68 -0.25 42.07 0.8 78.81 2.7 99.65
-1.4 8.08 -0.2 44.04 0.85 80.23 2.8 99.74
-1.3 9.68 -0.15 46.02 0.9 81.59 2.9 99.81
-1.2 11.51 -0.1 48.01 0.95 82.89 3 99.87
-1.1 13.57 0 50 1 84.13 3.5 99.98
Use the table above to find the standard score and percentile of: A) a data value 0.75 standard deviation below the mean; and B) a data value 3 standard deviations above the mean. Explain how you arrived at your answer in “your own” words.
Use the table above to find the approximate standard score of the following data values, then give the approximate number of standard deviations that the value lies above or below the mean. A) Data value in the third percentile. B) Data value in the 94th percentile.
To find the standard score and percentile of a data value, you can refer to the table provided.
A) To find the standard score and percentile of a data value that is 0.75 standard deviations below the mean, you can subtract 0.75 from the mean and locate the corresponding values in the table. In this case, the mean is represented by a standard score of 0.
So, to find the standard score, subtract 0.75 from 0 (mean). This gives you a standard score of -0.75. Now you can find the percentile associated with this standard score in the table. The percentile value for a standard score of -0.75 is not explicitly given in the table, but you can approximate it by looking at the values closest to it. In this case, the closest values are -0.8 (21.19 percentile) and -0.7 (24.2 percentile). Since -0.75 is closer to -0.8, you can estimate the percentile to be around 21.19.
Therefore, the standard score is -0.75 and the approximate percentile is 21.19.
B) To find the standard score and percentile of a data value that is 3 standard deviations above the mean, you can add 3 to the mean and locate the corresponding values in the table. In this case, the mean is represented by a standard score of 0.
So, to find the standard score, add 3 to 0 (mean). This gives you a standard score of 3. Now you can find the percentile associated with this standard score in the table. The percentile value for a standard score of 3 is 99.87.
Therefore, the standard score is 3 and the percentile is 99.87.
Now let's move on to determining the approximate standard score and number of standard deviations for given percentiles.
A) To find the approximate standard score for a data value in the third percentile, locate the percentile of 3 in the table. The closest available percentile is 2.9 (which has a standard score of -2.3) and 4.46 (which has a standard score of -1.7). Since 3 is closer to 2.9, you can estimate the standard score to be around -2.3.
Therefore, the approximate standard score for a data value in the third percentile is -2.3. To find the approximate number of standard deviations, you can subtract this standard score from the mean (which is 0 in this case). So, the data value is approximately 2.3 standard deviations below the mean.
B) To find the approximate standard score for a data value in the 94th percentile, locate the percentile of 94 in the table. The closest available percentile is 93.32 (which has a standard score of 1.5) and 94.52 (which has a standard score of 1.6). Since 94 is closer to 94.52, you can estimate the standard score to be around 1.6.
Therefore, the approximate standard score for a data value in the 94th percentile is 1.6. To find the approximate number of standard deviations, you can subtract this standard score from the mean (which is 0 in this case). So, the data value is approximately 1.6 standard deviations above the mean.