Descriptive Statistics

Use this data file (Muijs, 2011) to complete the following items/questions. Make sure to include the SPSS output in the word document. The SPSS output does not count in the page limit.

1. Identify one nominal, ordinal and continuous variable.
2. Run a frequency distribution for the variables school is funand sometimes I think I can’t do anything right. What findings do these two frequency distributions reveal to you?
3. What measure of central tendency would be the most appropriate to use to compare school is funand sometimes I think I can’t do anything right?  Report and interpret this central tendency measure for each variable.
4. What measure of central tendency would be the most appropriate to use for School Grades-Math and School Grades-English?  Report and interpret the variable comparison of these central tendency measures.
5. How would you compare the variability spread between School Grades-Mathand School Grades-English scores? What do your variability results reveal?
6. Find, justify and present one variable within the assignment SPSS dataset that is appropriate to construct a pie chart.

Solution 

The given data file contains 61 variables with 889 observations. The variables are of different types, like nominal or ordinal or scale variables. In order to explore frequency distribution and summary statistics for suitable variables, only few variables had been selected for the analysis and are described below:

The frequency distribution for Gender has been calculated and the corresponding result showed that 50.1% (i.e., 445 out of 889) are boys and 49.9% are girls (i.e., 444 out of 889). Similarly, the frequency distribution has been constructed for two ordinal variables “School is fun” and “sometimes I think I can’t do anything right” and the corresponding result shows the actual frequencies of each level of the variable along with the respective percentages. Since these two variables are ordinal in nature, these variables can be compared by the use of mode. In this case, a maximum of 38.4% of the students replied that they ‘agree strongly’ that their school is fun, while a maximum of 32.7% of the students answered that they ‘agree’ that “sometimes I think I can’t do anything right”.

The variable spread between two continuous variables can be examined by the use of standard deviation and coefficient of variation. In this case, the descriptive statistics have been calculated for the two continuous variables “School grades English” and “School grades Maths” and the corresponding results showed that the mean English score is 78.35 with the standard deviation of 10.42 and the mean Maths Score is 75.99 with the standard deviation of 12.21. The coefficient of variation is calculated by dividing Standard deviation by Mean. In this case, the coefficient of variable for English Score is 13.30% (=10.42/78.35) and that of Maths Score is 16.07% (= 12.21/75.99). It can be clearly seen that both the coefficient of variation for English Score is less than that of Maths Score, which indicates that the School Grade English is more consistent (or less variation) than School Grade Maths.

In addition to the descriptive statistics, a pie chart can be constructed for a nominal variable, namely ‘Type of School’. The variable ‘Type of School’ is a nominal variable with four levels (State, Catholic, COE, and Other), for which it is appropriate to use Pie chart as a graphical representation. The pie chart constructed for this variable is shown below:

From the above pie chart, it can be clearly seen that 69.40% of the schools are ‘State’, 18.90% of the schools are of type ‘Catholic’ and only 11.70% of the schools are of type ‘COE’.

Appendix

FREQUENCIES VARIABLES=attsc2 self6

/ORDER=ANALYSIS. 

Frequencie

Frequency Table

DESCRIPTIVES VARIABLES=enggrademathgrad

/STATISTICS=MEAN STDDEV MIN MAX. 

Descriptives

DESCRIPTIVES VARIABLES=enggrademathgrad

/STATISTICS=MEAN STDDEV VARIANCE MIN MAX. 

Descriptives

* Chart Builder.

GGRAPH

/GRAPHDATASET NAME=”graphdataset” VARIABLES=schtypeCOUNT()[name=”COUNT”] MISSING=LISTWISE REPORTMISSING=NO

/GRAPHSPEC SOURCE=INLINE.

BEGIN GPL

SOURCE: s=userSource(id(“graphdataset”))

DATA: schtype=col(source(s), name(“schtype”), unit.category())

DATA: COUNT=col(source(s), name(“COUNT”))

COORD: polar.theta(startAngle(0))

GUIDE: axis(dim(1), null())

GUIDE: legend(aesthetic(aesthetic.color.interior), label(“type of school”))

SCALE: linear(dim(1), dataMinimum(), dataMaximum())

SCALE: cat(aesthetic(aesthetic.color.interior), include(“1.00”, “2.00”, “3.00”, “4.00”))

ELEMENT: interval.stack(position(summary.percent(summary.percent(COUNT, base.all(acrossPanels())))), color.interior(schtype))

END GPL. 

GGraph

FREQUENCIES VARIABLES=gender

/ORDER=ANALYSIS. 

Frequencies