Psychology

Measures of central tendency are a group of descriptive statistics that measures the central values of a certain variable distribution. Measures of central tendency include three measures which are the mean, median and the mode. On the other hand, measures of variability are measures that determine the spread of a certain variable distribution. The most common measures of variability are variance and standard deviation. Both measures of central tendency and variability are used to describe the distribution of a certain variable numerically (Howell, 2008).

Other than central tendency and variability, skewness and kurtosis are measures also used to describe the distribution of data variable. Skewness measures the symmetry of a distribution. More precisely, skewness measures the lack of symmetry of a distribution. On the other hand, kurtosis is a measure that determines whether the distribution is flat or peaked (Howell, 2008).

Table 1
Descriptive Statistics
Descriptive StatisticsNRangeMinimumMaximumMeanStd. DeviationSkewnessKurtosisStatisticStatisticStatisticStatisticStatisticStatisticStatisticStd. ErrorStatisticStd. ErrorGPA in 9th Grade2163.75.254.002.4386.84507-.267.166-.572.3309th Grade English Grade2164.00.004.002.4954.90988-.211.166-.287.330IQ Score21682.0055.00137.00102.354212.55762-.114.166.333.330Gender2161.001.002.001.4630.49978.150.166-1.996.330Valid N (listwise)216 Table 1 shows some measures of central tendency, variability, skewness and kurtosis of GPA, IQ score, and Gender. From the table, one can see that the mean GPA is equal to 2.4386. This means that the average GPA for 9th grade is equal to 2.4386. On the other hand, the mean English grade is equal to 2.4954. The value of the mean suggests that the average English grade for 9th grade students is 2.4954. The mean IQ from the table was measured at 102.3542. The value means that the average IQ score of 9th grade students is equal to 102.3542. The mean for the gender value does not mean anything as gender is a nominal variable.

The standard deviation for the GPA is equal to 0.84507. The value means that GPA of 9th grade students spreads in an average of 0.84507 from the mean. The standard deviation for the English grade is equal to 0.90988. The value means that English grade of 9th grade students spreads in an average of 0.90988 from the mean. The standard deviation for the IQ score is equal to 12.5576. The value means that IQ score of 9th grade students spreads in an average of 12.5576 from the mean. The standard deviation for the gender variable is means nothing since the variable is a nominal variable.

The skewness and kurtosis for GPA are -0.267 and -0.572. The value means that the distribution of 9th grade GPA is slightly left tailed and is peaked. The skewness and kurtosis for English grade are -0.211 and -0.287. The value means that the distribution of 9th grade English grades is slightly left tailed and is peaked. The skewness and kurtosis for IQ score are -0.114 and 0.333. The value means that the distribution of 9th grade IQ scores is slightly left tailed and is peaked. The skewness and kurtosis for gender means nothing as gender is a nominal variable.

Table 2
Gender Comparison of IQ score
ReportIQ ScoreGenderMeanNStd. DeviationRangeKurtosisSkewnessMale99.439711612.7257382.00.914.001Female105.735010011.5260955.00-.348-.133Total102.354221612.5576282.00.333-.114 From the table 2, one can see that the mean IQ score of males is 99.4397. This means that the average IQ score of male 9th grade students is equal to 99.4397. The male IQ scores spread around the mean at an average of 12.72573. On the other hand, the mean IQ score of females is equal to 105.735. The value means that the average IQ score of female 9th grade students is equal to 105.735. The IQ scores of 9th grade female students are spread around the mean at an average of 11.52609. From the obtained means for male and female 9th grade students, it seems that females have greater IQ scores than male 9th grade students.

The skewness and kurtosis of male IQ score are equal to 0.914 and 0.001 respectively. This means that the distribution of male IQ scores is approximately symmetrical at the mean. While, the shape of the distribution is peaked. On the other hand, the skewness and kurtosis of female IQ score are equal to -0.348 and -0.133 respectively. The values mean that the distribution of female IQ scores is slightly left tailed and is peaked. The interpretation of skewness and kurtosis of male and female IQ scores reinforced the interpretation given based from the histograms of IQ scores separated based on gender.

The used of descriptive statistics has its strengths. The strengths of the used of descriptive statistics is that it helps in summarizing data for further analysis. In addition, descriptive statistics can be used to visually inspect normality of distributions. However, there are also limitations with the use descriptive statistics. From the name itself, descriptive statistics are only used to describe the distribution of a certain data. Descriptive statistics cannot be used to make inferences regarding the data itself. For example, the average mean IQ score of female 9th grade students is greater than male students. However, one cannot infer that the IQ scores of female 9th grade students are indeed higher than male students based on the descriptive statistics alone.