Urgent stastics question!!!

Question

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

Answer 1

Step 1) Arrange the data from low to high.

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

Then find the range (largest - smallest) or 98 - 51 = 47. Divide 47 by the number of groups and round up to the nearest digit. 47/6 = 7.833 and rounding up you get 8. Now, start with the lowest number (51) and add 8 to get to the first number of the next group, 51 + 8 = 59 so the starts of each group are:

51 59 67 75 83 91

Then make the end of each group the number just before the start of the next group

Low High

51 58

59 66

67 74

75 82

83 90

91 98

Step 2) count the number in each group:

Low High Freq

51 58 5

59 66 9

67 74 11

75 82 9

83 90 4

91 98 2

Step 3) To get the Relative Frequency, divide column 3 by the total number (40 in this case)

Low High Freq Rel Freq

51 58 5 0.125

59 66 9 0.225

67 74 11 0.275

75 82 9 0.225

83 90 4 0.1

91 98 2 0.05

Step 4) To get cumulative relative frequency, create column 5 which will be the sum of column 4 as you go down the table example, the second entry is 0.125 + 0.225 or 0.35 while the third entry is 0.125 + 0.225 + 0.275 or 0.625

Low High Freq Rel Freq CRF

51 58 5 0.125 0.125

59 66 9 0.225 0.35

67 74 11 0.275 0.625

75 82 9 0.225 0.85

83 90 4 0.1 0.95

91 98 2 0.05 1

The class boundaries are shown. The midpoints are halfway in between the upper and lower (51 + 58)/2 = 54.5

Using Excel is a little trickier. You will need to know how to work Excel to do this. But you'd get a chart like this: