Data and Probability

Weather data: PAGASA rainfall and temperature

Estadistika at probabilidad

Datos ng panahon: ulan at temperatura mula PAGASA

A year of monthly rainfall shows the wet and dry seasons; use it for temperature conversion, averages, range and spread.

Where it fits

Data and Descriptive Statistics · Term 2 · Week 2
Units and Conversion · Term 1 · Weeks 6–9
The Normal Distribution · Term 2 · Weeks 8–9

Competencies

gm11.t2.w2.c3 Identify the appropriate measure of central tendency and measures of variability of a given data set for different purposes.
gm11.t2.w2.c5 Interpret the computed measures of central tendency and variability.
gm11.t1.w9.c1 Apply temperature conversions to real-world scenarios such as recipe adjustments, weather reports, scientific experiments, storage conditions, and energy efficiency.

The data

Monthly rainfall and mean maximum temperature, Metro Manila station
Month	Rainfall (mm)	Mean max temp (°C)
Jan	18	30.1
Feb	12	31.0
Mar	26	32.6
Apr	34	34.2
May	131	34.1
Jun	257	32.6
Jul	432	31.3
Aug	486	30.8
Sep	355	31.1
Oct	232	31.3
Nov	129	31.0
Dec	72	30.0

Rainfall (mm) by Month

Source: Representative 2026 figures for classroom use; check current official rates before using for real decisions. Values follow the climatological pattern PAGASA publishes for Science Garden, Quezon City (Type I climate).

Scenario and worked example

Planning the Foundation Day

Engage

The SSLG wants an outdoor Foundation Day. Using the station's monthly data, when is the driest stretch? How hot will it be? The weather app shows 93°F for the planned date; what is that in Celsius?

Worked example: temperature conversion

Explain

C = \frac{5}{9}(F-32) = \frac{5}{9}(93-32) \approx 33.9°\text{C}

Centre and spread

Elaborate

The mean rainfall (182 mm) is far above the median (130 mm) because five wet-season months are extreme. The range (474 mm) and standard deviation describe how unequal the months are.

Looking ahead to the normal curve

Extend

Daily maximum temperatures in a month cluster around their mean with a bell shape. In Term 2 Weeks 8–9 you will use the mean and standard deviation to find the chance of a day hotter than, say, 36°C.

Discuss in class

Which months would you call 'dry'? Justify with the data, not just the names of the seasons.
Why might a tourist brochure quote the median rainfall rather than the mean?
Temperature varies by about 4°C across the year but rainfall varies by a factor of 40. Which measure of spread shows this better, range or percentage?

Problems

5 problems · check your answer, then open the solution

Problem 1 Basic

PAGASA reports a maximum temperature of 32°C in Manila. Convert this to degrees Fahrenheit.

Your answer (°F)
Show step-by-step solution
1. $F = \dfrac{9}{5}C + 32$ .
2. $F = \dfrac{9}{5}(32) + 32 = 57.6 + 32 = 89.6°\text{F}$ .
Answer: 89.6 °F
Problem 2 Standard

Monthly rainfall (mm) at a station: 18, 12, 26, 34, 131, 257, 432, 486, 355, 232, 129, 72. Find the mean monthly rainfall.

Your answer (mm)
Show step-by-step solution
1. Sum of the twelve values $= 2{,}184$ mm.
2. Mean $= 2{,}184 \div 12 = 182$ mm per month.
Answer: 182 mm
Problem 3 Basic

Using the same rainfall data (18, 12, 26, 34, 131, 257, 432, 486, 355, 232, 129, 72), find the range.

Your answer (mm)
Show step-by-step solution
1. Maximum is 486 mm (August); minimum is 12 mm (February).
2. Range $= 486 - 12 = 474$ mm.
Answer: 474 mm
Problem 4 Standard

The mean monthly rainfall is 182 mm but the median is 130 mm. What does this tell you about the distribution of rainfall across the year?

Choices a. Rainfall is about the same every month b. A few very wet months pull the mean above the typical month c. Most months are wetter than 182 mm d. The data must contain an error
Show step-by-step solution
1. Mean > median signals a right-skewed distribution.
2. Here the wet season (June–October) contributes very large values while the dry months are far below the mean.
Answer: b
Problem 5 Challenge

Daily maximum temperatures for a week (°C): 30, 32, 34, 31, 33. Find the population standard deviation to two decimal places.

Your answer (°C)
Show step-by-step solution
1. Mean $= (30+32+34+31+33)/5 = 32$ .
2. Squared deviations: $4, 0, 4, 1, 1$ ; sum $= 10$ .
3. Variance $= 10/5 = 2$ ; standard deviation $= \sqrt{2} \approx 1.41°\text{C}$ .
Answer: 1.41 °C

Data tool (statistics and charts) More practice: Data and Descriptive Statistics More practice: Units and Conversion More practice: The Normal Distribution