Question

4.) the following is average inches of rainfall for twenty cities in the us.
inches of rainfall per year
55 53 51 46 43 39 35 33 30 26
18 14 12 60 51 49 38 75 60 59
(a) use the table to create a frequency table to simplify the data.
inches of rainfall per year
classes tally frequency midpoint relative frequency cumulative frequency
10 - 20
20 - 30
30 - 40
40 - 50
50 - 60
60 - 70
70 - 80
(b) create a histogram for the data.

Explanation:

Step1: Count data in each class

For the class 10 - 20, the values 18, 14, 12 fall in this range. Tally: |||, Frequency = 3. Midpoint = $\frac{10 + 20}{2}=15$. Relative Frequency = $\frac{3}{20}=0.15$. Cumulative Frequency = 3.

Step2: Continue for other classes

For 20 - 30, no values in this range. Tally: 0, Frequency = 0. Midpoint = $\frac{20+30}{2}=25$. Relative Frequency = $\frac{0}{20}=0$. Cumulative Frequency = 3.
For 30 - 40, values 39, 35, 33, 30, 38. Tally: ||||, Frequency = 5. Midpoint = $\frac{30 + 40}{2}=35$. Relative Frequency = $\frac{5}{20}=0.25$. Cumulative Frequency = 3 + 5=8.
For 40 - 50, values 46, 43, 49. Tally: |||, Frequency = 3. Midpoint = $\frac{40+50}{2}=45$. Relative Frequency = $\frac{3}{20}=0.15$. Cumulative Frequency = 8+3 = 11.
For 50 - 60, values 55, 53, 51, 51, 59. Tally: |||||, Frequency = 5. Midpoint = $\frac{50+60}{2}=55$. Relative Frequency = $\frac{5}{20}=0.25$. Cumulative Frequency = 11 + 5=16.
For 60 - 70, values 60, 60. Tally: ||, Frequency = 2. Midpoint = $\frac{60+70}{2}=65$. Relative Frequency = $\frac{2}{20}=0.1$. Cumulative Frequency = 16+2 = 18.
For 70 - 80, value 75. Tally: |, Frequency = 1. Midpoint = $\frac{70+80}{2}=75$. Relative Frequency = $\frac{1}{20}=0.05$. Cumulative Frequency = 18+1 = 19.

The completed frequency table is:

Classes	TALLY	Frequency	Midpoint	Relative Frequency	Cumulative Frequency
20 - 30		0	25	0	3
30 - 40						5	35	0.25	8
40 - 50					3	45	0.15	11
50 - 60							5	55	0.25	16
60 - 70				2	65	0.1	18
70 - 80		1	75	0.05	19

To create a histogram:

• The x - axis represents the classes (10 - 20, 20 - 30, etc.)
• The y - axis represents the frequency.
• Draw bars for each class with height equal to the frequency of that class. For example, for the class 10 - 20, the bar has height 3, for 30 - 40 the bar has height 5 and so on. Since the class 20 - 30 has frequency 0, there is no bar for that class in the histogram.

Answer:

The completed frequency table is shown above and the steps to create the histogram are described above.