**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.

- Identify one nominal, ordinal and continuous variable.
- Run a frequency distribution for the variables
and*school is fun*. What findings do these two frequency distributions reveal to you?*sometimes I think I can’t do anything right* - What measure of central tendency would be the most appropriate to use to compare
and*school is fun*? Report and interpret this central tendency measure for each variable.*sometimes I think I can’t do anything right* - What measure of central tendency would be the most appropriate to use for
and*School Grades-Math*? Report and interpret the variable comparison of these central tendency measures.*School Grades-English* - How would you compare the variability spread between
and*School Grades-Math*scores? What do your variability results reveal?*School Grades-English* - 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:

Variable |
Type |

Gender (boy or girl) | Nominal |

School is fun (Disagree strongly to Agree strongly) | Ordinal |

School Grades-Math or
School Grades-English scores |
Continuous |

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**

gender |
|||||

Frequency | Percent | Valid Percent | Cumulative Percent | ||

Valid | boy | 445 | 50.1 | 50.1 | 50.1 |

girl | 444 | 49.9 | 49.9 | 100.0 | |

Total | 889 | 100.0 | 100.0 |

school is fun |
|||||

Frequency | Percent | Valid Percent | Cumulative Percent | ||

Valid | disagree strongly | 141 | 15.9 | 15.9 | 15.9 |

disagree | 142 | 16.0 | 16.0 | 31.9 | |

agree | 263 | 29.6 | 29.7 | 61.6 | |

agree strongly | 341 | 38.4 | 38.4 | 100.0 | |

Total | 887 | 99.8 | 100.0 | ||

Missing | 9 | 2 | .2 | ||

Total | 889 | 100.0 |

sometimes I think I can’t do anything right |
|||||

Frequency | Percent | Valid Percent | Cumulative Percent | ||

Valid | agree strongly | 113 | 12.7 | 12.8 | 12.8 |

agree | 291 | 32.7 | 32.8 | 45.6 | |

disagree | 218 | 24.5 | 24.6 | 70.2 | |

disagree strongly | 264 | 29.7 | 29.8 | 100.0 | |

Total | 886 | 99.7 | 100.0 | ||

Missing | 9 | 3 | .3 | ||

Total | 889 | 100.0 |

Descriptive Statistics |
||||||

N | Minimum | Maximum | Mean | Std. Deviation | Variance | |

school grades English | 575 | 31.00 | 96.60 | 78.3472 | 10.41636 | 108.500 |

school grades maths | 575 | 30.00 | 98.80 | 75.9874 | 12.21432 | 149.190 |

Valid N (listwise) | 575 |

FREQUENCIES VARIABLES=attsc2 self6

/ORDER=ANALYSIS.** **

**Frequencie**

Statistics |
|||

school is fun | sometimes I think I can’t do anything right | ||

N | Valid | 887 | 886 |

Missing | 2 | 3 |

**Frequency Table**

school is fun |
|||||

Frequency | Percent | Valid Percent | Cumulative Percent | ||

Valid | disagree strongly | 141 | 15.9 | 15.9 | 15.9 |

disagree | 142 | 16.0 | 16.0 | 31.9 | |

agree | 263 | 29.6 | 29.7 | 61.6 | |

agree strongly | 341 | 38.4 | 38.4 | 100.0 | |

Total | 887 | 99.8 | 100.0 | ||

Missing | 9 | 2 | .2 | ||

Total | 889 | 100.0 |

sometimes I think I can’t do anything right |
|||||

Frequency | Percent | Valid Percent | Cumulative Percent | ||

Valid | agree strongly | 113 | 12.7 | 12.8 | 12.8 |

agree | 291 | 32.7 | 32.8 | 45.6 | |

disagree | 218 | 24.5 | 24.6 | 70.2 | |

disagree strongly | 264 | 29.7 | 29.8 | 100.0 | |

Total | 886 | 99.7 | 100.0 | ||

Missing | 9 | 3 | .3 | ||

Total | 889 | 100.0 |

DESCRIPTIVES VARIABLES=enggrademathgrad

/STATISTICS=MEAN STDDEV MIN MAX.** **

**Descriptives**

Descriptive Statistics |
|||||

N | Minimum | Maximum | Mean | Std. Deviation | |

school grades English | 575 | 31.00 | 96.60 | 78.3472 | 10.41636 |

school grades maths | 575 | 30.00 | 98.80 | 75.9874 | 12.21432 |

Valid N (listwise) | 575 |

DESCRIPTIVES VARIABLES=enggrademathgrad

/STATISTICS=MEAN STDDEV VARIANCE MIN MAX.** **

**Descriptives**

Descriptive Statistics |
||||||

N | Minimum | Maximum | Mean | Std. Deviation | Variance | |

school grades English | 575 | 31.00 | 96.60 | 78.3472 | 10.41636 | 108.500 |

school grades maths | 575 | 30.00 | 98.80 | 75.9874 | 12.21432 | 149.190 |

Valid N (listwise) | 575 |

* 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**

Statistics |
||

gender | ||

N | Valid | 889 |

Missing | 0 |

gender |
|||||

Frequency | Percent | Valid Percent | Cumulative Percent | ||

Valid | boy | 445 | 50.1 | 50.1 | 50.1 |

girl | 444 | 49.9 | 49.9 | 100.0 | |

Total | 889 | 100.0 | 100.0 |