Question

Suppose the researcher has collected data from a sample of 150 individuals for this study. For
each individual, the weekly take-home pay and weekly food expenditure were recorded. The
data is stored in the file FOODEXP.XLS. Using this data set and EXCEL, answer the questions
below.

Take-home pay   Weekly food expenditure
262   82
369   182
374   144
381   161
378   210
395   126
401   196
410   212
408   130
415   151
418   145
415   171
425   156
116   114
120   102
124   79
130   127
132   78
139   50
266   100
234   115
237   64
242   60
247   187
251   141
253   146
258   191
104   45
110   84
271   180
274   134
279   111
281   103
145   67
151   86
156   47
160   124
166   89
170   51
174   125
228   162
229   60
541   250
555   179
561   271
562   204
567   245
569   169
571   205
576   256
588   247
590   205
600   180
600   225
560   245
565   232
598   228
614   239
620   199
853   279
892   270
893   320
891   316
894   350
927   333
848   356
852   336
861   269
867   282
987   359
990   281
430   225
433   162
443   149
449   172
486   198
484   183
482   217
491   212
500   231
514   219
513   235
516   247
518   242
524   160
527   179
372   166
374   109
381   188
382   189
398   141
372   188
375   118
380   156
381   152
394   123
360   146
360   118
764   307
769   303
775   270
786   254
801   250
847   340
849   295
821   318
636   260
639   274
644   238
645   263
646   256
652   223
657   218
727   314
827   267
831   267
832   323
835   310
749   255
758   315
668   296
668   255
680   246
683   299
683   296
689   308
691   290
696   249
720   310
721   273
287   83
289   93
295   81
297   167
304   188
306   76
309   165
315   100
320   159
321   115
361   131
372   166
373   112
378   113
381   99
394   112
360   155
985   278
1050   370
1095   373


First, the researcher wishes to use the graphical descriptive methods and numerical descriptive
measures to present the data for the two variables.
(a) The researcher decides to use 8 class intervals such as 100<X≤225, 225<X≤350, 350<X≤475,
….., 975<X≤1100 for weekly take-home pay variable and class intervals 0<X≤50, 50<X≤100,
100<X≤150, …. , 350<X≤400 for weekly food expenditure variable. Explain how the researcher
would have decided on 8 class intervals.
(b) Draw a histogram for each variable using appropriate BIN values from part (a).

Answer 1

Result:

First, the researcher wishes to use the graphical descriptive methods and numerical descriptive
measures to present the data for the two variables.
(a) The researcher decides to use 8 class intervals such as 100<X≤225, 225<X≤350, 350<X≤475,
….., 975<X≤1100 for weekly take-home pay variable and class intervals 0<X≤50, 50<X≤100,
100<X≤150, …. , 350<X≤400 for weekly food expenditure variable. Explain how the researcher
would have decided on 8 class intervals.

	Take-home pay	Weekly food expenditure
n	150	150
minimum	104	45
maximum	1095	373
range	991	328

From the given class interval, width of the class interval for Take-home pay is 125. Range of the data is 991.

The range/ width of the class interval gives approximate number of class intervals.

For Take-home pay, 991/125=7.92. This is approximated to 8 class intervals.

For Weekly food expenditure, 328/50=6.56. This is approximated to 7 class intervals. Since we are taking the lower limit of the first class is 0, and maximum value is 373, we need 8 classes.

(b) Draw a histogram for each variable using appropriate BIN values from part (a).

Frequency Distribution - Quantitative
		Take-home pay						cumulative
	lower		upper	midpoint	width	frequency	percent	frequency	percent
	100	<	225	163	125	15	10.0	15	10.0
	225	<	350	288	125	25	16.7	40	26.7
	350	<	475	413	125	35	23.3	75	50.0
	475	<	600	538	125	24	16.0	99	66.0
	600	<	725	663	125	21	14.0	120	80.0
	725	<	850	788	125	16	10.7	136	90.7
	850	<	975	913	125	9	6.0	145	96.7
	975	<	1,100	1,037	125	5	3.3	150	100.0
						150	100.0

Frequency Distribution - Quantitative
		Weekly food expenditure						cumulative
	lower		upper	midpoint	width	frequency	percent	frequency	percent
	0	<	50	25	50	2	1.3	2	1.3
	50	<	100	75	50	17	11.3	19	12.7
	100	<	150	125	50	29	19.3	48	32.0
	150	<	200	175	50	32	21.3	80	53.3
	200	<	250	225	50	25	16.7	105	70.0
	250	<	300	275	50	26	17.3	131	87.3
	300	<	350	325	50	14	9.3	145	96.7
	350	<	400	375	50	5	3.3	150	100.0
						150	100.0