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
Frequency	2	4	3	3	7	3

The mean (¯xx¯) rain intensity: ____ inches (Please show your answer to 1 decimal place.)

The median rain intensity: ____ inches

The mode rain intensity: _____ inches (Please separate your answers by ',' in bimodal situation. Enter DNE if there is no mode.)

Answer 1

Let x indicate the inches of rain and f indicate the frequency

the mean of x is

ans: the mean rain intensity is 3.8 inches

Median: First we find the cumulative frequencies as below

Inches of Rain	Frequency	Cumulative Frequency
1	2	2
2	4	6
3	3	9
4	3	12
5	7	19
6	3	22
Total	22

First

n=22 is the number of observations.

If n is odd, the median is (n+1)/2 st observation

If n is even, the median is the average of n/2 nd and n/2+1st observations

Here n=22 is even. n/2ns observation is 22/2=11th observation. n/2+1th observation is the 12th observation.

Using the cumulative frequency, we can say that the number of observations till 3 inches of rain is 9 and the number of observations till 4 inches of rain is 12. That is the 11th and 12th observations have a value of 4 inches.

The median is the average of (4+4)/2=4

ans: The median rain intensity is 4 inches.

The mode is the observation with highest frequency.

We can see that 5 inches of rain has been observed 7 times. No other observation has frequency as high as 7. Hence the mode is 5 inches.

ans: The mode rain intensity: 5 inches