4.6 Data, Measurement, and Everyday Statistics

Data and Measurement in Real Contexts

The Functional Numeracy strand of CASAS reaches past money math into data, measurement, and everyday statistics - the numbers adults meet in health records, recipes, work logs, utility usage, and household budgets. The reading discipline is the same as for charts: read the labels, units, and scale first, then match the question word to the operation. The math is rarely hard once the setup is right; nearly every wrong answer comes from a unit slip or from confusing two statistics that sound similar.

Tables and multi-series displays

A table is a grid of rows and columns. The first move is to find the intersection the question wants: the right row and the right column. A weekly hours table with employees down the side and days across the top answers "How many hours did Ana work Wednesday?" at one cell - Ana's row, Wednesday's column. A multi-series chart (a double-bar or two-line graph) adds a legend; trace the correct series before reading a value. "How much more electricity than water in March" requires the solid (electricity) value minus the dashed (water) value at March - a difference, not a sum.

Everyday statistics: mean, median, mode, range

Four summary numbers appear often, and CASAS distractors usually swap one for another:

The order step for the median is non-negotiable: an unordered list gives a wrong middle. With an even count, the median is the average of the two middle values. A question that asks for the "most common" delivery time wants the mode, while "typical" or "average" wants the mean - reading the question word decides which.

Measurement and unit conversion

Measurement items cover length, weight, volume, time, and temperature. Convert to a common unit before comparing or adding. Keep these exact facts ready:

• Length: 1 foot = 12 inches; 1 yard = 3 feet; 1 mile = 5,280 feet.
• Weight: 1 pound = 16 ounces; 1 ton = 2,000 pounds.
• Volume: 1 gallon = 4 quarts = 8 pints = 16 cups; 1 cup = 8 fluid ounces.
• Time: 1 hour = 60 minutes; 1 day = 24 hours; 1 week = 7 days.
• Metric: units step by tens - 1 kilometer = 1,000 meters; 1 meter = 100 centimeters; 1 kilogram = 1,000 grams; 1 liter = 1,000 milliliters.

A recipe that needs 3/4 cup per batch for 4 batches needs 3/4 x 4 = 3 cups. A board cut into 8-inch pieces from a 6-foot board first converts 6 feet to 72 inches, then 72 / 8 = 9 pieces. Mixing feet and inches without converting is the classic measurement error.

Simple probability

CASAS probability is the chance of a favorable outcome out of the total outcomes, written as a fraction, decimal, or percent. If a bag holds 3 red and 5 blue marbles, the chance of drawing red is 3 out of 8 total = 3/8 = 0.375 = 37.5%. The trap is using only the favorable count (3) or only the other count (5) as the denominator instead of the total (8). A spinner with 4 equal sections has a 1/4 = 25% chance on any one section.

Matching the question word to the operation

Worked example: a small data set

A delivery log shows packages delivered over five days: 12, 15, 15, 18, 20. The mean is (12+15+15+18+20)/5 = 80/5 = 16. The median, with the values already in order, is the middle value, 15. The mode is 15 (it appears twice). The range is 20 - 12 = 8. Four different but correct answers come from one data set, which is exactly why the question word must be read before computing. A learner who reports 16 when the question asked for the most common count has done correct arithmetic for the wrong statistic.

A reliable data-and-measurement routine

• Read labels, units, legend, and scale before any number.
• For a table, lock onto the row-and-column intersection the question names.
• Convert to one unit before comparing, adding, or dividing.
• Match the question word to mean, median, mode, range, or probability - do not assume "average."
• Estimate the answer's size so a unit slip or a swapped statistic stands out as unreasonable.

Reading temperature, time, and elapsed-time items

Measurement on CASAS includes temperature and elapsed time, both common in health and work contexts. A thermometer or weather chart may ask for a difference: a fever of 101 degrees against a normal 98.6 is a 2.4-degree difference, found by subtraction, not by reading one value alone.

Elapsed time asks how long something lasts: a shift from 8:45 a.m. to 5:15 p.m. is 8 hours 30 minutes, and the trap is subtracting the clock numbers (5 minus 8) instead of counting forward across noon. Count whole hours first (8:45 to 4:45 is 8 hours), then the extra minutes (4:45 to 5:15 is 30 minutes). Crossing noon or midnight is where careless answers appear.

Percent of a quantity in data items

Data displays frequently ask for a percent of a total: what share of 200 surveyed customers chose a product, or what percent of a monthly budget goes to rent. Convert the percent to a decimal and multiply, or set up a part-over-whole fraction. If 50 of 200 customers chose option A, that is 50/200 = 0.25 = 25 percent. The reverse item gives the percent and the whole and asks for the part: 15 percent of a $1,200 budget is 0.15 x 1,200 = $180. The trap is reading the raw count (50) when the question asked for the percent, or vice versa - read the question word, count or percent, before answering.

Putting reading, units, and the question word together

A single data item often layers all three skills: read a multi-series chart correctly (the right line), convert to a common unit if the values differ, then apply the operation the question word demands.

A utility chart in kilowatt-hours compared against a cost in dollars cannot be subtracted directly - one is energy, one is money. Keeping the unit attached to every number is the safeguard that catches a mismatched subtraction before it becomes a wrong answer. Data and measurement items reward the same evidence-first habit as the rest of CASAS: read the display correctly, choose the operation the words demand, and keep the units honest from the first step to the last.