Estadistika at probabilidad

ILAW Daily Lesson Log (DLL)

Making Sense of Data: Descriptive Statistics

Data and Descriptive Statistics · Term 2 · Week 2

Word (.docx)

Learning area: General Mathematics
Designed by: SSHS Math Talas Hub
Grade level and section: Grade 11
Sessions / term: 4 sessions · Term 2
References: DepEd Grade 11 Three-Term Budget of Work (BOW) for General Mathematics
Philippine Statistics Authority (PSA) OpenSTAT public datasets
The jamovi project (2024). jamovi (Version 2.5) [Computer software]. https://www.jamovi.org
Galamay, D.O., & Albay, E.M. (2026). General Mathematics: A Strengthened Senior High School Textbook. Diwa Learning Systems Inc.
Digital tools: jamovi, Google Sheets, Calculator
Declaration of AI use (DO 3, s. 2026 Annex A): AI was used only as an auxiliary support tool in preparing and improving this lesson plan, in accordance with DepEd Order No. 003, s. 2026. The teacher retained human judgment and full responsibility for content selection, contextualization, assessment decisions, learner feedback, and final approval. AI-generated suggestions were reviewed, edited, and checked for accuracy, bias, appropriateness, data privacy, and alignment with the Learning Competencies. No learner personal data were entered into AI tools, and AI will not be used as the sole basis for grading, learner evaluation, disciplinary decisions, or other major academic decisions.

Intentions

Learning competency

Identify different types of data and classify a given set of data according to its level of measurement.

gm11.t2.w2.c1, gm11.t2.w2.c2

Learning objectives

At the end of the 45-minute period, the learners should be able to:

distinguish qualitative from quantitative (discrete and continuous) data;
classify variables as nominal, ordinal, interval or ratio with justification; and
value careful data collection that respects privacy.

Learner context

Learners have made bar graphs and computed averages in junior high. They tend to call anything numeric 'quantitative' and have not met levels of measurement. A quick class survey of harmless variables gives a shared dataset for the whole week.

Learning experience

Pre-lesson

Hook

Engage

Is a jersey number a quantity? If player 20 is 'twice' player 10, what would that mean?

Activity: Class Survey

Elicit

Learners fill an anonymous slip: travel time to school (minutes), number of siblings, favourite subject, mode of transport, and how much they agree that 'math is useful' (1–5). Collect and project the raw data.

Flow

Explore: Sort the variables

Explore

Groups sort the five survey variables (plus cards: temperature, ZIP code, birth year, shoe size, grade level) into categories of their own and name the categories.

"What rule did you use?"
"Can you add or subtract two values meaningfully? Can you say one is twice another?"

Explain: Types and levels

Explain

Introduce qualitative vs quantitative (discrete, continuous), then the four levels of measurement, mapping learners' own categories onto them. Use the 'doubling test' for ratio and the 'true zero' question for interval.

Level	Order?	Equal gaps?	True zero?	Example
Nominal	no	no	no	mode of transport
Ordinal	yes	no	no	agreement 1–5
Interval	yes	yes	no	temperature °C
Ratio	yes	yes	yes	travel time

Elaborate: Enter the data in jamovi

Elaborate

Pairs type the survey data into jamovi (or Sheets) and set each variable's measurement type. Observe which statistics jamovi offers for each type and explain why.

Learning resources

Anonymous survey slips
Variable cards
jamovi (free) or Google Sheets; printed data table as backup
Level-of-measurement organizer

Opportunities for integration

ICT: Data entry and variable types in jamovi.
Research (Practical Research): Variables and measurement in survey design.
Values: Anonymity and data privacy.

Assessment

Formative assessment

Exit Ticket

Evaluate

Classify three new variables (daily allowance, barangay name, pain scale 0–10) by type and level, with one reason each.

Accommodation: organizer with guiding questions for each level.

Ways forward

Extended learning opportunities

Variables Around Me

Extend

List eight pieces of information on a product label or a school form and classify each by type and level of measurement.

Reflections

Think about what you need to change for the next session based on what happened today.

Day 1

Intentions

Learning competency

Identify different types of data and classify a given set of data according to its level of measurement.

gm11.t2.w2.c1, gm11.t2.w2.c2

Learning objectives

At the end of the 45-minute period, the learners should be able to:

distinguish qualitative from quantitative (discrete and continuous) data;
classify variables as nominal, ordinal, interval or ratio with justification; and
value careful data collection that respects privacy.

Learner context

Learning experience

Pre-lesson

Hook

Engage

Is a jersey number a quantity? If player 20 is 'twice' player 10, what would that mean?

Activity: Class Survey

Elicit

Flow

Explore: Sort the variables

Explore

Groups sort the five survey variables (plus cards: temperature, ZIP code, birth year, shoe size, grade level) into categories of their own and name the categories.

"What rule did you use?"
"Can you add or subtract two values meaningfully? Can you say one is twice another?"

Explain: Types and levels

Explain

Level	Order?	Equal gaps?	True zero?	Example
Nominal	no	no	no	mode of transport
Ordinal	yes	no	no	agreement 1–5
Interval	yes	yes	no	temperature °C
Ratio	yes	yes	yes	travel time

Elaborate: Enter the data in jamovi

Elaborate

Pairs type the survey data into jamovi (or Sheets) and set each variable's measurement type. Observe which statistics jamovi offers for each type and explain why.

Learning resources

Anonymous survey slips
Variable cards
jamovi (free) or Google Sheets; printed data table as backup
Level-of-measurement organizer

Opportunities for integration

ICT: Data entry and variable types in jamovi.
Research (Practical Research): Variables and measurement in survey design.
Values: Anonymity and data privacy.

Assessment

Formative assessment

Exit Ticket

Evaluate

Classify three new variables (daily allowance, barangay name, pain scale 0–10) by type and level, with one reason each.

Accommodation: organizer with guiding questions for each level.

Ways forward

Extended learning opportunities

Variables Around Me

Extend

List eight pieces of information on a product label or a school form and classify each by type and level of measurement.

Reflections

Think about what you need to change for the next session based on what happened today.

Day 2

Intentions

Learning competency

Identify the appropriate measure of central tendency of a given data set for different purposes.

gm11.t2.w2.c3

Learning objectives

At the end of the 45-minute period, the learners should be able to:

compute mean, median and mode of a data set;
select the measure of centre that fits the data type and purpose, and justify it; and
recognise how an extreme value affects each measure.

Learner context

Learners can compute the mean and have met median and mode but see them as alternative formulas rather than tools for different purposes. The class survey dataset includes at least one extreme travel time, which drives the lesson.

Learning experience

Pre-lesson

Hook

Engage

The mean travel time of our class is 24 minutes, but most of you said 10–20. Who is the 'typical' learner?

Activity: Line Up

Elicit

Learners line up by travel time. Find the middle person physically. Compare with the mean on the board.

Flow

Explore: Move one value

Explore

Groups compute mean, median and mode of the travel times, then change the largest value to 300 minutes and recompute. Record which measures moved and by how much.

\bar{x} = \dfrac{\sum x}{n}

Explain: Purpose decides the measure

Explain

Consolidate: mean uses every value (good for totals, pulled by extremes); median describes the typical case; mode is the only option for nominal data. Connect to levels of measurement from Day 1.

Data / purpose	Best measure	Why
Favourite subject (nominal)	mode	only category frequency makes sense
Incomes with a few very rich	median	resistant to extremes
Total rice needed from average consumption	mean	mean × n gives the total

Elaborate: Which Student Is Correct?

Elaborate

Student A: 'The average Filipino household earns the mean income, so most families earn that much.' Student B: 'Most families earn less than the mean because a few earn very much.' Decide using a small income list.

Learning resources

Class survey data
Calculator
jamovi or Sheets
Centre-selection worksheet

Opportunities for integration

Araling Panlipunan: Income distribution and inequality.
ICT: Descriptive statistics in jamovi.
Critical Thinking: Evaluating claims that use 'average'.

Assessment

Formative assessment

Exit Ticket

Evaluate

Given house prices in a subdivision (₱1.2M, ₱1.3M, ₱1.3M, ₱1.5M, ₱9M), compute all three measures and state which a buyer should quote as 'typical', and why.

Accommodation: data pre-sorted for learners who need support finding the median.

Ways forward

Extended learning opportunities

Average Claims

Extend

Find one advertisement or news item that uses 'average'. Which measure do you think they used? Would another measure tell a different story?

Reflections

Think about what you need to change for the next session based on what happened today.

Day 3

Intentions

Learning competency

Identify appropriate measures of variability and use appropriate technologies to calculate measures of central tendency and variability.

gm11.t2.w2.c3, gm11.t2.w2.c4

Learning objectives

At the end of the 45-minute period, the learners should be able to:

compute range and standard deviation by table and with jamovi or Sheets;
explain standard deviation as a typical distance from the mean; and
check technology output against a hand computation.

Learner context

Learners can choose a measure of centre but have no measure of spread beyond 'the scores are different'. They have entered data in jamovi once. The step-by-step deviation table makes the standard deviation concrete before the software produces it instantly.

Learning experience

Pre-lesson

Hook

Engage

Two sections both have a quiz mean of 8. In one, everyone scored 7–9; in the other, scores ran from 2 to 10. Does the mean tell the whole story?

Activity: Dot Plots

Elicit

Learners sketch dot plots of both sections' scores and write one word describing each.

Flow

Explore: How far from the mean?

Explore

Groups compute each score's deviation from the mean for a five-value set, notice the deviations sum to zero, then square them, average (divide by n − 1) and take the square root. Compare with the range.

s = \sqrt{\dfrac{\sum (x - \bar{x})^2}{n - 1}} = \sqrt{7} \approx 2.65

x	x − x̄	(x − x̄)²
6	−3	9
8	−1	1
8	−1	1
10	1	1
13	4	16

Explain: Range and standard deviation

Explain

Formalise range and sample standard deviation; interpret s as 'typical distance from the mean'. Note that jamovi reports the sample SD (n − 1).

Elaborate: Let the software do it, then check

Elaborate

Pairs run Exploration → Descriptives in jamovi on the class travel-time data (mean, median, mode, SD, range) and in Sheets use AVERAGE, MEDIAN, MODE, STDEV, MAX−MIN. They verify one value by hand and reconcile any difference.

Learning resources

jamovi or Google Sheets
Calculator
Deviation table worksheet
Class survey data

Opportunities for integration

ICT: Descriptives in jamovi; statistical functions in Sheets.
Science: Variability in repeated measurements.
Critical Thinking: Verifying software output.

Assessment

Formative assessment

Exit Ticket

Evaluate

For 4, 7, 7, 10, 12: compute range and standard deviation by table; then write one sentence interpreting s in context (daily sales of a vendor, in units).

Accommodation: pre-filled first two rows of the deviation table.

Ways forward

Extended learning opportunities

Consistency Counts

Extend

Record the minutes you spend commuting (or doing homework) for five days. Compute mean and standard deviation. Are you consistent?

Reflections

Think about what you need to change for the next session based on what happened today.

Day 4

Intentions

Learning competency

Interpret the computed measures of central tendency and variability.

gm11.t2.w2.c5, gm11.t2.w2.c3

Learning objectives

At the end of the 45-minute period, the learners should be able to:

interpret centre and spread together in the context of a real dataset;
produce a short data report with an appropriate chart and justified choices; and
critique a peer's interpretation using the rubric.

Learner context

Learners can classify data and compute centre and spread by hand and with technology. They are ready to interpret results for an audience and defend their choice of measures with an authentic dataset (PSA open data or the class survey).

Learning experience

Pre-lesson

Hook

Engage

A barangay captain asks: 'How long do our students travel to school, and is it the same for everyone?' Answer in two sentences using statistics.

Flow

Concept Reconstruction

Elicit

Groups rebuild the week's map from memory: Data type → Level → Measure of centre → Measure of spread → Interpretation.

Performance Task: Mini Data Report

Elaborate

Each group picks a dataset (class survey variable, or a small PSA table such as regional rice prices or provincial rainfall). They classify it, choose and compute centre and spread in jamovi or Sheets, make one chart, and write a five-sentence interpretation for a non-mathematician.

State the type and level of measurement.
Name the measures you chose and why.
Report values with units and a chart.
Interpret centre and spread together.
State one limitation of your data.

Peer Review

Evaluate

Groups exchange reports and score with the rubric, writing one strength and one question. Authors revise one sentence based on feedback.

Learning resources

Class survey data and small PSA datasets (printed)
jamovi or Google Sheets
Rubric and peer-review form
Chart paper or slides

Opportunities for integration

ICT: Charts and descriptives in jamovi/Sheets.
Practical Research: Reporting descriptive results.
Communication: Writing for a non-technical audience.

Assessment

Formative assessment

Rubric-scored report

Evaluate

The mini data report is scored with the rubric; peer-review notes serve as evidence of interpretation skills.

Ways forward

Extended learning opportunities

Data in the News

Extend

Find a news chart or statistic about your province. Identify the measure used and write a two-sentence interpretation that includes something about spread, if possible.

Reflections

Think about what you need to change for the next session based on what happened today.

Rubric: Mini data report

Criteria	Weight
Correct identification of data type and level of measurement	15%
Appropriate choice of centre and spread, with reason	25%
Accurate computation (jamovi/Sheets output matches hand check)	20%
Interpretation in context, in plain language	25%
Clear table or chart and presentation	15%
Total	100%

Teaching notes and common misconceptions

Learners classify any number as quantitative. Jersey numbers, ZIP codes and Likert ratings are numerals used as labels or ranks. Ask 'does doubling it mean twice as much?' to test for interval/ratio level.
The mean is treated as 'the average' for every situation. Use a barangay income list with one very rich household to show the mean leaving the typical household behind, and let learners choose the median themselves.
Mode is often reported as the frequency (how many) instead of the value that occurs most often.
Standard deviation is read as 'how far from the mean every value is'. Build it from deviations in a table first so learners see it as a typical distance, and connect range to the same question.
In jamovi, learners may forget to set the variable's measurement type (nominal/ordinal/continuous), which changes the available statistics. Treat this as a formative check of level of measurement.
Collect only non-sensitive class data (e.g., travel time, number of siblings, favourite subject). Do not collect family income or grades.

Worked examples

Example 1: Classifying data

Classify each: (a) favourite subject, (b) satisfaction rating 1–5, (c) temperature in °C, (d) monthly allowance in pesos.

(a) qualitative, nominal
(b) qualitative in nature but ranked: ordinal
(c) quantitative, interval (0 °C is not 'no temperature')
(d) quantitative, ratio (₱0 means none; ₱400 is twice ₱200)

Example 2: Choosing the centre

Travel times (minutes): 5, 10, 10, 15, 20, 20, 25, 90.

\bar{x} = \dfrac{195}{8} = 24.4

\text{median} = \dfrac{15 + 20}{2} = 17.5

\text{mode} = 10 \text{ and } 20

The 90-minute learner pulls the mean above seven of the eight learners; the median (17.5 min) describes the typical learner better.

Example 3: Standard deviation by table

Quiz scores: 6, 8, 8, 10, 13 (mean 9).

s = \sqrt{\dfrac{28}{4}} = \sqrt{7} \approx 2.65

Scores are typically about 2.6 points from the mean of 9; the range is 7.

x	x − x̄	(x − x̄)²
6	−3	9
8	−1	1
8	−1	1
10	1	1
13	4	16

Example 4: Interpreting two sections

Section A: mean 80, s = 3. Section B: mean 80, s = 12.

Both sections have the same average, but Section B's scores are far more spread out: some learners scored very high and others very low.
A teacher would plan differentiated support in Section B and whole-class pacing in Section A.