LET Secondary Assessment of Learning — Statistics, Grading and Interpreting Assessment ResultsSummary

The mean is the sum of all scores divided by the number of scores (ΣX / n). It is the most commonly used measure of central tendency because it uses every data point. However, it is highly sensitive to extreme values (outliers); if one student scores 20 when others score 80+, the mean drops significantly. Example: Seven students score 82, 85, 85, 88, 90, 92, 94. Sum = 616; mean = 616 ÷ 7 = 88. In a positively skewed distribution, the mean is pulled toward the high tail and sits above the median.

The median is the middle score when all scores are arranged in order. If there is an even number of scores, the median is the average of the two middle values. Example: In the set 82, 85, 85, 88, 90, 92, 94 (n=7), the 4th score is 88, so the median = 88. The median is not affected by outliers or extreme skewness, making it a more representative measure than the mean for skewed distributions. The median is always the 50th percentile (P50) and the second quartile (Q2).

The mode is the score that appears most often in the dataset. A distribution can be unimodal (one mode), bimodal (two modes of equal frequency), or have no mode if all scores appear equally often. Example: In 82, 85, 85, 88, 90, 92, 94, the mode is 85 because it appears twice. The mode is the only measure of central tendency suitable for nominal (categorical) data, such as the most common response option chosen by students or the most frequent learning competency needing reteaching.

The range is the simplest measure of spread: highest score minus lowest score. In the example 82, 85, 85, 88, 90, 92, 94, the range = 94 - 82 = 12. The range is quick to calculate but crude because it depends only on the two extreme scores and ignores the distribution of scores in between. A class where scores range from 50 to 100 has the same range as a class with scores 50, 50, 50, 100, 100, 100, yet the distributions look very different.

Standard deviation is the average distance of scores from the mean. Conceptually, to calculate SD: (1) find each score's deviation from the mean, (2) square each deviation, (3) sum the squared deviations, (4) divide by n to get the variance, (5) take the square root to get the SD. Example: Five scores 4, 6, 8, 10, 12 have a mean of 8. Deviations: -4, -2, 0, +2, +4. Squared: 16, 4, 0, 4, 16. Sum = 40. Variance = 40 ÷ 5 = 8. SD = √8 ≈ 2.83. Interpretation: on average, scores sit about 2.8 points away from the mean of 8. A small SD means scores cluster tightly (homogeneous group); a large SD means scores are scattered (heterogeneous group).

Percentiles divide an ordered distribution into 100 equal parts. A percentile rank of 90 (P90) means a student scored as well as or better than 90% of the group—NOT that the student answered 90% of items correctly. Quartiles divide the distribution into four parts: Q1 = P25 (25th percentile), Q2 = P50 (50th percentile = median), Q3 = P75 (75th percentile). The interquartile range (IQR = Q3 - Q1) represents the spread of the middle 50% of scores and is not affected by outliers. Deciles (D1-D9) divide the distribution into ten parts; D5 = P50 = Q2 = median. The LET loves testing the equivalence P50 = Q2 = D5 = median.

The normal curve is a theoretical, symmetrical, bell-shaped distribution that many large sets of human traits approximate. In a perfect normal distribution: (1) mean = median = mode (all at the center), (2) the curve is symmetrical, (3) tails approach but never touch the baseline (asymptotic), (4) about 68% of scores lie within ±1 SD of the mean, about 95% within ±2 SD, and about 99.7% within ±3 SD (the 68-95-99.7 rule). Example: A test with mean 80 and SD 5 has roughly 68% of scores between 75 and 85 (one SD on each side) and roughly 95% between 70 and 90 (two SDs).

Skewness describes asymmetry in a distribution and is named after the direction of the tail, not the direction of the hump. **Positively skewed (skewed right):** The tail points toward the high (right) end; most scores cluster at the low end. This means the test was difficult, and the class struggled. In a positive skew, **mean > median > mode**. **Negatively skewed (skewed left):** The tail points toward the low (left) end; most scores cluster at the high end. This means the test was easy, and the class performed well. In a negative skew, **mean < median < mode**. The mean always gets dragged toward the tail (the outliers pull it). **Symmetric (normal):** mean = median = mode; the test had balanced difficulty. This is the most tested topic on the LET; the trap is confusing which tail direction indicates an easy versus hard test.

The z-score converts a raw score to a standardized score that indicates how many standard deviations the score lies above (+) or below (-) the mean. Formula: z = (X - mean) / SD. The z distribution has a mean of 0 and an SD of 1. Example: A class has mean 80, SD 4. Ana scores 88: z = (88-80)/4 = +2.0 (two SDs above the mean, roughly top 2% if distribution is normal). Ben scores 76: z = (76-80)/4 = -1.0 (one SD below the mean, roughly the lower 16%). z-scores allow fair comparison of performance across tests with different means, SDs, and even number of items. The interpretation is: a z of +1.5 means the student performed 1.5 standard deviations better than the class average.

The T-score is a standard score that eliminates negative values, making communication with parents clearer. Formula: T = 50 + 10z. The T distribution has a mean of 50 and an SD of 10. Example: Ana's z = +2.0 gives T = 50 + 10(2) = 70. Ben's z = -1.0 gives T = 50 + 10(-1) = 40. A T of 60 is one SD above average (z = +1.0); a T of 40 is one SD below (z = -1.0). T-scores are often used on standardized tests and psychological instruments because they are easier to interpret than z-scores (no negative numbers) and scale to a familiar mean of 50.

A correlation describes the linear relationship between two variables. It carries two pieces of information: (1) **Direction:** Positive correlation (variables move together: higher study time → higher grades); negative correlation (variables move oppositely: higher absences → lower grades); near-zero correlation (no linear relationship). (2) **Strength:** r ranges from -1.00 to +1.00. Strength is measured by absolute value: |r| near 0.00-0.20 = negligible, 0.21-0.40 = low, 0.41-0.60 = moderate, 0.61-0.80 = high, 0.81-1.00 = very high. Example: r = -0.85 (strong negative) is stronger than r = +0.60 (moderate positive) because |-0.85| > |+0.60|. The critical warning: **correlation does not imply causation.** A negative correlation between library visits and test scores does not mean the library causes poor scores; perhaps students with learning gaps visit the library more.

DepEd Order No. 8, s. 2015 is the national policy governing classroom assessment and grading for the K to 12 Basic Education Program. It mandates a standards-based, competency-based grading system with three components: (1) **Written Work (WW):** Quizzes, unit tests, essays, short written outputs. (2) **Performance Tasks (PT):** Projects, experiments, demonstrations, presentations, portfolios—anything showing learner application of knowledge. (3) **Quarterly Assessment (QA):** The culminating exam or performance given at the end of the quarter. Each component is assigned a weight depending on the subject. Example for Grade 3-10 Math: WW = 40%, PT = 40%, QA = 20%. For Languages: WW = 30%, PT = 50%, QA = 20%. Notice that Performance Tasks carry heavy weight everywhere, reflecting the learner-centered philosophy of K-12. The quarterly grade is computed as: [(WW% × 0.40) + (PT% × 0.40) + (QA% × 0.20)] = initial grade. The initial grade is then **transmuted** (converted) using a table where 100 transmutes to 100 and 60 transmutes to 75 (the minimum passing grade). The final grade in a subject is the simple average of the four quarterly grades.

After calculating an initial grade (the weighted average of WW, PT, and QA percentages), the initial grade is converted using a transmutation table. This table maps initial percentages to reported grades on a 0-100 scale. The key features: An initial grade of 100 transmutes to 100; an initial grade of 60 transmutes to 75 (the passing grade). Scores below 60 remain as-is or transmute to 60, the lowest reported grade on the report card. This transformation ensures that 75 is the agreed minimum for passing in the Philippine system. Grade descriptors are: 90-100 = Outstanding (O), 85-89 = Very Satisfactory (VS), 80-84 = Satisfactory (S), 75-79 = Fairly Satisfactory (FS), Below 75 = Did Not Meet Expectations (DNM). A learner with an initial grade of 63 (poor performance on the weighted average) transmutes to 75 (FS/passing); a learner with an initial grade of 80 transmutes to approximately 85-87 (VS), showing non-linear scaling at the lower end.

DepEd Order No. 8, s. 2015 specifies different weights for Written Work, Performance Tasks, and Quarterly Assessment depending on the subject, recognizing that different subjects require different types of assessment. **For Grades 1-10:** Mathematics and Science: WW 40%, PT 40%, QA 20%; Languages (Filipino, English): WW 30%, PT 50%, QA 20%; Araling Panlipunan (Social Studies): WW 30%, PT 50%, QA 20%; MAPEH (Music, Arts, PE, Health) and EPP/TLE: WW 20%, PT 60%, QA 20%; EsP (Values): WW 30%, PT 50%, QA 20%. **Senior High School** (Grades 11-12) uses different weights by academic track (e.g., STEM, HUMSS) and is found in separate DepEd guidelines. Notice that all subjects weight Performance Tasks heavily (minimum 40%), reflecting DepEd's emphasis on competency and application over memorization.

To compute a quarterly grade under DepEd Order No. 8, s. 2015: **(1) Collect raw scores** for all Written Work items, Performance Task items, and the Quarterly Assessment (exam/performance). **(2) Convert each component to a percentage:** WW% = (sum of WW raw scores / total possible WW points) × 100; same for PT and QA. **(3) Multiply each percentage by the component weight:** WW weighted = WW% × weight; PT weighted = PT% × weight; QA weighted = QA% × weight. **(4) Sum the weighted scores:** Initial Grade = WW weighted + PT weighted + QA weighted. **(5) Transmute the initial grade** using the DepEd transmutation table to get the reported quarterly grade. **Example (Grade 4 Math):** WW raw = 45/50 = 90%; PT raw = 38/50 = 76%; QA raw = 18/20 = 90%. Using weights WW 40%, PT 40%, QA 20%: Initial = (90 × 0.40) + (76 × 0.40) + (90 × 0.20) = 36 + 30.4 + 18 = 84.4. An initial grade of 84.4 transmutes to approximately 86 (VS), the reported grade.

The final grade in a subject is the simple average of the four quarterly grades (Q1, Q2, Q3, Q4). Final Grade = (Q1 + Q2 + Q3 + Q4) / 4. A learner passes the subject if the final grade is 75 or above. If the final grade is below 75 in any subject (core or elective), DepEd policy requires remediation or retention depending on school and learner circumstances. Some schools offer summer remedial classes for failing learners, while others retain a learner in the same grade level if multiple subjects are failed. Teachers are responsible for documenting learning gaps and recommending appropriate intervention under RA 7836 (duty to support learner progress) and RA 7610 (special protection for children in need of intervention).

Measures of central tendency (mean, median, mode) tell you where scores center, but they don't tell you how spread out the scores are. Two classes can have the same mean of 80 but very different spreads: one tightly clustered (small SD, homogeneous) and another sprawling (large SD, heterogeneous). A complete description requires both. Example: Grade 3 Section A has mean 80, SD 2 (tight cluster, probably well-taught content). Grade 3 Section B has mean 80, SD 15 (wide scatter, mixed ability or uneven instruction).

In a symmetric (normal) distribution, mean = median, so either works. In a positively skewed distribution (few high scores, many low scores), the mean is pulled up by the outliers, while the median stays closer to where most students actually scored. Report the median in this case because it better represents the typical student. In a negatively skewed distribution (many high scores, few low scores), the mean is pulled down, so again the median is more representative. Teachers use skewness to decide what to report to parents about class performance.

If a distribution is approximately normal, you can use the 68-95-99.7 rule and a standard normal table to estimate percentile ranks from z-scores. A z-score of +1.0 corresponds to roughly P84 (because 68% ÷ 2 = 34% from the mean to +1 SD, plus 50% below the mean = 84%). A z-score of 0 corresponds to exactly P50 (the mean, the median, the 50th percentile). This relationship allows quick estimation of how extreme a score is.

Raw scores from different tests or subjects cannot be compared directly because the tests may have different means, SDs, and maximum points. Converting to z-scores or T-scores puts them on the same scale. Carlo scored 85 in Math and 88 in English; his z-scores show that he performed better in Math relative to his class (z = +1.0) than in English (z = +0.5), even though his raw English score is higher.

Written Work (WW) captures learning through low-stakes quizzes and quick checks; Performance Tasks (PT) measure application and higher-order thinking through projects and presentations; Quarterly Assessment (QA) is the summative measure. By weighting all three, DepEd ensures that grades reflect broad evidence of learning, not just exam performance. A student who struggles on QA but excels in PT can still earn a passing grade because PT carries significant weight (especially in languages and social studies: 50%).

An initial grade of 63% (a failing score on most scales) transmutes to 75 (FS, passing) because DepEd defines 75 as the national standard for adequate performance. This non-linear transmutation at the lower end reflects a policy choice: learners who show partial mastery are helped to meet the standard, not immediately failed. Grade descriptors (O, VS, S, FS, DNM) add meaning so that a parent hears 'Very Satisfactory' not just a number.

Both range and SD quantify how spread out scores are. Range is quick but depends only on the two extreme scores and ignores the middle. SD averages the deviations of all scores from the mean, making it more stable and informative. A class with scores 50, 75, 85, 95, 100 has the same range (100-50=50) as a class with 50, 50, 50, 100, 100, 100, but very different SDs, because the first is more evenly distributed.

Percentiles (100 intervals) and quartiles (4 intervals) serve the same function at different granularities. A student at P75 is in Q3 (the 75th percentile, the third quartile). Teachers use these to identify high performers (P90+), average performers (P40-P60), and low performers (P20 and below) and tailor instruction accordingly.

When you give the same test twice (test-retest reliability), you calculate the correlation between the two administrations. If students' relative rankings are stable (high performers score high both times, low performers score low both times), the correlation is high, and the test is reliable. Similarly, criterion-related validity is measured by correlating test scores with a criterion (e.g., report card grades). Teachers use correlation to understand if their assessments are consistent and valid measures of learning.