Question

in california, we need more rain to sustain the health of our natural environment, argriculture, and economic. a group of statistics students in oxnard college recorded the amount of rain during 2016-2017 school year, measuring the intensity by the inches of rain, and the results were:

inches of rain	1	2	3	4	5	6

the mean ($\bar{x}$) rain intensity: $\square$ inches (please show your answer to 1 decimal place.)

the median rain intensity: $\square$ inches

the mode rain intensity: $\square$ inches (please separate your answers by , in the bimodal situation. enter dne if there is no mode or if there are more than two modes.)

Explanation:

Mean Calculation

Step1: Calculate total inches (x*f)

For each row, multiply inches (x) by frequency (f):

• \(1 \times 3 = 3\)
• \(2 \times 2 = 4\)
• \(3 \times 6 = 18\)
• \(4 \times 3 = 12\)
• \(5 \times 4 = 20\)
• \(6 \times 7 = 42\)

Step2: Sum total inches and total frequency

Total inches: \(3 + 4 + 18 + 12 + 20 + 42 = 99\)
Total frequency: \(3 + 2 + 6 + 3 + 4 + 7 = 25\)

Step3: Compute mean (\(\bar{x} = \frac{\text{Total inches}}{\text{Total frequency}}\))

\(\bar{x} = \frac{99}{25} = 3.96 \approx 4.0\) (to 1 decimal)

Median Calculation

Step1: Find cumulative frequency

• For \(x=1\): \(3\) (cumulative: \(3\))
• \(x=2\): \(2\) (cumulative: \(3 + 2 = 5\))
• \(x=3\): \(6\) (cumulative: \(5 + 6 = 11\))
• \(x=4\): \(3\) (cumulative: \(11 + 3 = 14\))
• \(x=5\): \(4\) (cumulative: \(14 + 4 = 18\))
• \(x=6\): \(7\) (cumulative: \(18 + 7 = 25\))

Step2: Locate median position (\(\frac{n+1}{2} = \frac{25+1}{2} = 13\))

Find the smallest cumulative frequency ≥ 13. Cumulative frequency for \(x=4\) is 14 (≥13), so median is \(4\).

Mode Calculation

Step1: Identify highest frequency

Frequencies: \(3, 2, 6, 3, 4, 7\). The highest frequency is \(7\), corresponding to \(x=6\).

Answer:

s:
Mean: \(4.0\) inches
Median: \(4\) inches
Mode: \(6\) inches