Question

the following is the average daily temperature for portland, oregon for the month of july:
70 72 90 86 83 82
93 81 94 85 85 73
82 94 82 74 80 85
93 70 76 87 91 70
72 86 79 79 90 94
(a) complete the frequency distribution for the data. (use 4 decimal places when applicable)
temperature frequency relative frequency cumulative frequency cumulative relative frequency
70 - 74 7
75 - 79 3
80 - 84 6
85 - 89 6
90 - 94 8
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Explanation:

Step1: Calculate total frequency

The total frequency is the sum of all individual frequencies: $7 + 3+6 + 6+8=30$.

Step2: Calculate relative frequencies

For the $70 - 74$ range: Relative frequency = $\frac{7}{30}\approx0.2333$.
For the $75 - 79$ range: Relative frequency = $\frac{3}{30}=0.1000$.
For the $80 - 84$ range: Relative frequency = $\frac{6}{30}=0.2000$.
For the $85 - 89$ range: Relative frequency = $\frac{6}{30}=0.2000$.
For the $90 - 94$ range: Relative frequency = $\frac{8}{30}\approx0.2667$.

Step3: Calculate cumulative frequencies

For the $70 - 74$ range, cumulative frequency is $7$.
For the $75 - 79$ range, cumulative frequency is $7 + 3=10$.
For the $80 - 84$ range, cumulative frequency is $10+6 = 16$.
For the $85 - 89$ range, cumulative frequency is $16+6=22$.
For the $90 - 94$ range, cumulative frequency is $22 + 8=30$.

Step4: Calculate cumulative relative frequencies

For the $70 - 74$ range, cumulative relative frequency = $\frac{7}{30}\approx0.2333$.
For the $75 - 79$ range, cumulative relative frequency = $\frac{10}{30}\approx0.3333$.
For the $80 - 84$ range, cumulative relative frequency = $\frac{16}{30}\approx0.5333$.
For the $85 - 89$ range, cumulative relative frequency = $\frac{22}{30}\approx0.7333$.
For the $90 - 94$ range, cumulative relative frequency = $\frac{30}{30}=1.0000$.

Answer:

Temperature	Frequency	Relative Frequency	Cumulative Frequency	Cumulative Relative Frequency
75 - 79	3	0.1000	10	0.3333
80 - 84	6	0.2000	16	0.5333
85 - 89	6	0.2000	22	0.7333
90 - 94	8	0.2667	30	1.0000