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Directions: Use the bell curve document under Content to answer the following questions 1-5.

  1. An IQ of 100 means what? An IQ of 120 is what percentile rank?

An Intelligence Quotient (IQ) test is a technique of measuring reasoning abilities of a person applied to clarify the level of one’s intelligence (“Meaning of an IQ Score,” 2014). An IQ of 100 is the generally accepted average standard. To put it in other words, this index proves that those who passed the testing are not gifted but quite intelligent to be well-performing in studying. Drawing upon the Bell Curve under analysis, percentile for an IQ of 120, which is above average intelligence, can be counted as follows: half of those who got IQs of a range of 115 to 130 – 6.80 (rounded) plus deviation IQs from zero to 115

6.80+0.13%+2.14%+13.59%+34.13%+34.13%=90.92%, meaning that students with IQs of 120 performed better than 90.92% of the class, which is the 92th percentile.

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  1. What percent of the population has IQs between 85 and 100? What implications might this have in the general education classrooms, high-stakes testing, accommodations, etc…?

About 34.13% of test-takers have an IQ level ranging from 85 to 100, which means their results are below the average or equal to average. However, lowered IQ test results do not prove that students are doomed to failure in studying (King, n. d.). Hence, closer examination and additional cognitive assessment tools have to be taken into account, such as Wechsler Intelligence scale, which estimates individual’s intellectual performance rather than capacity as compared to IQ tests. With respect to this model, children having the aforementioned IQ level are of low average to average intelligence. Students with such scores are “still within expectations of the general public” (King, n. d.). Thus, application of the modified teaching strategies (e.g. remediation) would be useful. In this regard, teachers have to assess and clarify the areas of concern for these children and address them foremost.

  1. What percent of the population has an IQ of less than 70? What does that mean in relation to education in America at this time? You can write an answer in response to adequate yearly progress (AYP) and the reauthorization of the Elementary and Secondary Education Act (ESEA). Think in terms of students being alternately assessed for AYP.

Following the Bell-shaped Curve data, 2.27% of the population has an IQ lower than 70, which evidence not only the Extremely Low range but also “a possibility of an Intellectual disability or Mental Retardation” (King, n. d.). Nonetheless, a closer examination and assessment of such children is necessary. The U.S. government implements specific policies toward such students, which are defined within the scope of the revised ESEA and AYP practice. In this way, children with such learning disabilities are able to take tests sensitive to their needs in accordance with individualized educational program while learning with ordinary students (U.S. Department of Education, n. d.).

  1. A student has a score on a reading test of 90. The mean is 85 and the standard deviation is 5 for the standardized assessment. What is the z score? What percentile rank is the student’s score? What might this mean to a general education teacher?

To calculate z score, the following formula is to be used z = (X – M) ÷ SD, where X = 85, M = 90, and SD = 5. As a result, z = (85 – 90) ÷ 5 = -1. Therefore, the percentile can be equal to 0.13%+2.14%+13.59%=15.98%. In this case, a general education teacher should clarify the gaps in the student’s knowledge and develop teaching strategies in order to fill in these gaps whereas the student’s results are still in the scope of general expectations.

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  1. A student’s overall academic achievement is 85. The same student’s IQ is 130. The mean for both tests is 100 and the standard deviation for both is 15. What would this information mean in terms of a potential learning disability for this student? Explain.

The results provided are quite controversial. On the one hand, the student’s IQ level refers to the Superior or the gifted range, indicating one’s high cognitive abilities (King, n. d.). On the other hand, the student’s overall academic achievement shows one’s Low Average range. The data does not obligatory demonstrates that a student has got a learning disability. On the contrary, it may be an indicator of some factor, which has prevented a student from performing well. In this regard, a teacher should clarify this factor that may be based within the learning context (e.g. home and community environment, learning material delivery, motivation, social-emotional behavior, etc.).


Directions: Use the document under Content “Aptitude Test Scores” to answer questions 6-9.

  1. Explain the correlation coefficients of 1.000 in the Table 2. What does it mean?

The correlation coefficient (r) defines relation between variables and is ranged from -1.0 to +1 (in the case study – 1.000). Whereas all correlation coefficients in Table 2 are positive, it means that the larger one variable is the other gets larger as well. In addition, correlation 1.000 is a perfect one. However, it should not be assumed that changes with respect to one variable can inevitably cause transformations in another one. Moreover, tests performed within similar areas of knowledge (e.g. either math/quantitative or verbal) are likely to show the highest correlation rates and vice versa. For instance, SAT-Math-to-SAT-Verbal demonstrate r .62, which means their correlation is low – 36% approximately – since they are poorly related.

  1. Which of the tests listed has the most variability? How do you know that (what do you look at to decide that)? Provide the score(s) you are using to make that determination.

Scores of the tests of the similar nature show the most relation, while those of different nature provide the most varying results. To put it in other words, SAT-Math versus GRE-Quantitative coefficients demonstrate relatedness – .86, which in percentage means 81% of the related variance. To be more precise, when SAT-Math results increase, GRE-Qualitative scores are likely to rise too. Conversely, correlation between SAT-Math and GRE-Verbal is estimated to be .6 (rounded) or 36%, proving the most variability in terms of the items contrasted. The same can be evidenced by GRE-Analytical-to-SAT-Verbal correlation. In this case, r is also .6 (rounded) or 36% squared.

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  1. What two tests have the highest correlation coefficient? Provide the correlation coefficient. Describe what it means. Explain why those two tests might be highly correlated. (Highest correlation coefficient other than the 1.0.)

If variables of similar nature are considered, their correlation is the most informative and evidences the highest correlation level. Specifically, correlation between SAT-Verbal and GRE-Verbal is .86. It is better understood when squared: e.g. an r value of .86 (.9 rounded) means 81% of the variance is related. The similar picture can be drawn with regard to GRE-Qualitative-to-SAT-Math correlation, which is .86 or 81% as well. The situation occurred due to that these tests assess students’ knowledge within similar areas, i.e. math or verbal proficiency, thus providing similar results concerning correlation.

  1. What two tests have the lowest correlation coefficient? Provide the correlation coefficient. Describe what it means. Explain why those two tests might have a low correlation.

As it has been previously indicated, test scores comparison regarding unrelated fields of study show that r is low. In particular, GRE-Verbal-to-SAT-Math and GRE-Quantitative-to-SAT-Verbal are the least correlated variables: rounded .6 or squared 36%. In this way, it is possible to assert that correlation coefficient evidences that GRE-Verbal test results are not related to those of SAT-Math. This correlation is low due to that variables are of different nature.

Inferential Statistics

Directions: Obtain the document under Content for this week labeled “Ninth Grade Students,” and use it to answer the questions below.

  1. Look at Extracurricular Activities in Table 1. What is the mean score for participation for ninth graders at the junior high school setting? What is the mean score for participation for ninth graders at the senior high school setting? At what probability level is there a difference between those two means? In yours words, what does that mean in relation to the first purpose statement?

Overall, the mean can be calculated as division of sum of all values observed on the number of observations. Therefore, the mean score for participation in extracurricular activities for ninth graders is 2.68 at the junior high school setting (JHS) and 1.99 at the senior high school (SHS). Probability value p is estimated as .01, which means that there is 99% of probability – (1-.01= .99) that these hypotheses are true. In this regard, ninth graders at JHS are more likely to participate in extracurricular activities as compared to those of SHS.

  1. Look at Overall grade point average (GPA) in Table 1. What is the mean score for GPA for ninth graders at the junior high school setting? What is the mean score for GPA for ninth graders at the senior high school setting? At what probability level is there a difference between those two means? In yours words, what does that mean in relation to the second purpose statement?

GPA results of ninth graders in JHS are also relatively higher than those of in JHS as evidenced by means: 2.59 to 2.24 respectively. In addition, the actual probability value of these data is .01, which is 99% (1-.01= .99). Consequently, the second purpose of the research has been justified in this way.

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  1. Look at Attitude Toward Self and School in Table 1. What is the mean score for the attitudes for ninth graders at the junior high school setting? What is the mean score for attitudes for ninth graders at the senior high school setting? What was the initial probability statistic where there was no significant difference between these two means? In yours words, what does that mean in relation to the third purpose statement?

Researching the attitude toward self and school demonstrates such means: 77.87 for ninth graders in JHS and 78.12 for SHS students. The p value for the test is different and is estimated as .05, namely (1-.05=.95) 95% probability that these indexes are true. Although the p value is a little lower here as compared to previously considered hypotheses, its meaning is still extremely significant. In this way, the results evidence that SHS ninth graders have higher rates of attitudes toward self and school.

  1. In your opinion, do the results reported here support the placement of ninth grade students in junior high school instead of senior high school? Explain in relation to all three purpose statements.

Irregardless of that JHS ninth graders have been found more active extracurricular activities participants and observably higher GPA rates as those of SHS, their mean of attitudes toward self and school are lower. In this regard, it is possible to assume that JHS students are ready to study well and be active out of the lessons’ scope, but their socialization levels are low. Thus, ninth graders should not be placed to SHS instead of JHS whereas their self and school attitudes are not well formulated and shaped enough at that age period.

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