Question

Answer questions 33, 34, and 35 on separate sheets of paper and turn in with your scantron.

The ages of the Vice Presidents of the United States at the time of their death are listed below. Construct a frequency distribution to summarize the data. Use 6 classes. List the relative and cumulative frequencies. List the class boundaries and class midpoints. Use Excel to construct a histogram to display the data.

90	83	80	73	70	51	68	79	70	71	72
74	67	54	81	66	62	63	68	57	66	96
78	55	60	66	57	71	60	85	76	98	77
88	78	81	64	66	77	70

Refer to the data set in question 33 above. Construct a stem and leaf plot to depict the ages of the vice-presidents at the time of their deaths.

Use EXCEL to construct a Pareto chart for the number of tons (in millions) of trash recycled per year by Americans based on an Environmental Protection Agency study.

Type	Amount
Paper	320
Iron/steel	282
Aluminum	268
Yard waste	242
Glass	196
Plastics	42

Answer 1

Histogram

Classes	Frequency	Cumulative Frequency	Relative Frequency	Lower Boundaries	Upper Boundaries	Midpoints
50 - 58	5	5	0.125	50	58	54
59 - 67	10	15	0.25	59	67	63
68 - 76	11	26	0.275	68	76	72
77 - 85	10	36	0.25	77	85	81
86 - 94	2	38	0.05	86	94	90
95 - 103	2	40	0.05	95	103	99
Total	40		1

Cumulative Frequency :- Adding the frequency with the preceding frequency i.e

Classes	Frequency	Cumulative Frequency
50 - 58	5	5 ( 5 as it is )
59 - 67	10	15 ( 5 + 10)
68 - 76	11	26 ( 11 + 15)
77 - 85	10	36 ( 10 + 26)
86 - 94	2	38 ( 2 + 36)
95 - 103	2	40 ( 2 + 38)

Relative Frequency :- Frequency / Sum of frequency

Classes	Frequency	Relative Frequency
50 - 58	5	0.125 ( 5 / 40)
59 - 67	10	0.25 ( 10 / 40 )
68 - 76	11	0.275 (11 / 40 )
77 - 85	10	0.25 (10 / 40)
86 - 94	2	0.05 ( 2 / 40)
95 - 103	2	0.05 ( 2 / 40)
Total	40	1

Midpoint :- ( Lower boundaries + Upper boundaries ) / 2

Classes	Lower Boundaries	Upper Boundaries	Midpoints
50 - 58	50	58	54 ( 50 + 58)/2
59 - 67	59	67	63 (59 + 67)/2
68 - 76	68	76	72 (68 + 76)/2
77 - 85	77	85	81 (77 + 85)/2
86 - 94	86	94	90 (86 + 94)/2
95 - 103	95	103	99 (95 + 103)/2

Construct a stem and leaf

Arrange the data in ascending order and take tens place digit as stem and ones place digit as leaf

Stem	Leaf
1
2
3
4
5	1 4 5 7 7
6	0 0 2 3 4 6 6 6 6 7 8 8
7	0 0 0 1 1 2 3 4 6 7 7 8 8 9
8	0 1 1 3 5 8
9	0 6 8

Pareto chart

Type	Amount	Cumulative Frequency	Percentage
Paper	320	320	24% (320 / 1350)
Iron/steel	282	602	45%  (602 / 1350)
Aluminum	268	870	64%  (870 / 1350)
Yard waste	242	1112	82%  (1112 / 1350)
Glass	196	1308	97%  (1308 / 1350)
Plastics	42	1350	100%  (1350 / 1350)
Total	1350

• Plot the bar graph in excel taking Amount and percentage
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