Part 2
The researcher wishes to use graphical descriptive methods and numerical descriptive measures to present the data for the two variables in various summary forms.
(a) The researcher decides to use 7 class intervals, such as 0<X≤15, 15<X≤30, ….. for the Exam mark variable and 0<X≤2, 2<X≤4, ….., for the study time variable. Explain how he/she could have decided on the number of class intervals as 7.
(b) Draw two histograms for the two variables using appropriate BIN values.
(c) Prepare a brief numerical summary report for the two variables; study time and exam mark by including the summary measures, such as mean, median, variance, standard deviation, smallest and largest values, and the three quartiles, for each variable.
(d) Based on your histograms in part (b) and descriptive summary measures in part (c), comment on the shape of the distribution of the two variables.
(e) Construct a relative frequency distribution for the two variables. Briefly comment on the relative frequency distribution.
(f) Construct a cumulative relative frequency distribution for the two variables. Briefly comment on the cumulative relative frequency distribution.
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a)
According to 2k rule,
2k >= n;
where ‘k’ is the number of classes
‘n’ is the number of data points.
Here, n = 110. For k=7, 27 = 128 which is just greater than n=110.
The width of a class interval is determined by:
Thus, it is sufficient to use 7 class intervals, such as 0<X≤15, 15<X≤30, ….. for the Exam mark variable and 0<X≤2, 2<X≤4, ….. , for the study time variable.
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