A negative z score indicates measurement is smaller than the mean while a positive z score says that the measurement is larger than the mean. Example: A teacher gives a test and the class average is 74 with a standard deviation of 6.

If a z-score is equal to 0, it is on the mean. A positive z-score indicates the raw score is higher than the mean average. A negative z-score reveals the raw score is below the mean average. For example, if a z-score is equal to -2, it is 2 standard deviations below the mean.

If a data value has a z-score of 2, that tells us that this data value is 2 standard deviations larger than the mean. A negative z-score means the data value is smaller than the mean. If a data value has a z-score of –3.1, then this data value is 3.1 standard deviations smaller than the mean.

Conversion of Raw score into Percentile score

1. STEP 1: ENTER THE SCORES THAT YOU WANT TO CONVERT IN TO PERCENTILE.
2. SORT THE DATA INTO ASCENDING ORDER TO CHECK FOR THE RANKS.
3. THIS IS THE ASCENDINGLY SORTED DATA.
4. CLICK TRANSFORM> RANK CASES, TO RANK THE DATA.
5. MAKE A TICK MARK IN RANK BRACKET AND PRESS CONTINUE.
6. THIS IS HOW YOU GET THE RANK FOR EACH SCORE OF RAW DATA.

The percentile is transformed from a raw score. It will give you a relative position, for example, 1 to 99. The numbers = the percentage of scores below your raw score. Obtaining a percentile rank of 80 means that whatever your raw score was, 80% of the other raw scores were below yours.

Highly gifted: 145 to 159. Exceptionally gifted: 160 to 179. Profoundly gifted: 180 or higher.

Stanine Scores A stanine score ranges from a low of 1 to a high of 9; therefore, the name “stanine.” For instance, a stanine score of 1, 2, or 3 is below average; 4, 5, or 6 is average; and 7, 8, or 9 is above average.

Stanine scores of 7 or 8 are usually interpreted as indicating “above average” performance. And a stanine score of 9 is normally considered to reflect “outstanding” performance, for that’s the highest score one can get.

9

If you know that your score is in the 90th percentile, that means you scored better than 90% of people who took the test. The 50th percentile is generally the median (if you’re using the third definition—see below). The 75th percentile is also called the third quartile.

Looking at the bell curve you can see the mean or average is 100 like our normed standardized bell curve. As you can see, 130 and up is considered Gifted, 115-129 is High intelligence, 85-114 is considered in the average range, 70-84 is borderline, and 69 and lower is extremely low IQ.

While the standard score of 90 is below the statistical mean of 100 and is at the 25th percentile, this performance is still within the average range and generally does not indicate any need for concern.

The top of the curve shows the mean, mode, and median of the data collected. Its standard deviation depicts the bell curve’s relative width around the mean.

The correct answer is that 43.32 percent of data is included in +/- 1.5 Sigma, which is answer choice A.

A z-score of 1.5 is 1.5 standard deviations above and below the mean. A z-score of 0 is no standard deviations above or below the mean (it’s equal to the mean).

692.5