Variables: What Does Each Record Describe? — Worked Solutions
Worked Solutions
Compare your reasoning with the worked solutions after attempting the questions. A different valid representation or explanation can earn credit when it satisfies the stated criteria.
Original generated practice for the Fall 2026 course. Return to the lesson and independent checks.
Read the rows: worked answer
A table has one row for each city bus and columns for route label, passenger count at noon, a sound recording of the engine, and a driver comment.
Part a
Identify the observational unit and two variables. Explain how the sound recording and text could convey meaningful data.
The bus is the observational unit. Route label and noon passenger count are variables; recording-derived noise level or engine-sound category and comment-derived issue category could also be variables. The recording and comment supply information that can be coded or measured using a defined rule.
| Evidence for credit | Points |
|---|---|
| Identifies bus and two changing characteristics. | 1 |
| Explains useful measurement/coding from both sound and text. | 1 |
Parameter or statistic?: worked answer
The mean age of every bus in the city fleet is unknown. A sample of 15 buses has a mean age of 6.4 years.
Part a
Identify the parameter and the statistic. Explain why 6.4 years need not equal the population mean and why it may still be useful.
The mean age of all buses in the city fleet is the parameter. The sample mean 6.4 years is the statistic. Different subsets can have different means, so the statistic need not equal the unknown parameter. A suitable sampling design can make it useful for estimating the fleet mean.
| Evidence for credit | Points |
|---|---|
| Distinguishes population mean and sample mean. | 1 |
| Explains possible inequality and inference role. | 1 |
Numbers can be labels: worked answer
A delivery record gives postcode 40712, distance 8.6 km, number of parcels 4, and vehicle category “van.”
Part a
Classify each recorded variable as categorical (qualitative) or quantitative (numerical). For each quantitative variable, state its unit or counted item. Explain why the postcode remains categorical even though it contains digits.
Postcode and vehicle category are categorical labels. Distance is quantitative in kilometres. Parcel count is quantitative in parcels. Arithmetic on a postcode does not measure an amount.
| Evidence for credit | Points |
|---|---|
| Correctly classifies all four; accepts categorical/qualitative and quantitative/numerical as synonymous names. | 1 |
| Gives kilometres and parcels, with label reasoning. | 1 |
Countable is not the same as small: worked answer
Consider (i) the number of occupied seats in a 40-seat bus, (ii) an idealized whole-number event count with no upper bound, and (iii) the underlying time, in seconds, for a bus trip.
Part a
Classify the quantitative variables as discrete or continuous. Explain finite and countably infinite possibilities and what values are possible between two distinct trip times.
Occupied seats is discrete with 41 possible values, 0 through 40. The ideal event count is discrete with countably infinite values 0,1,2,… . Underlying trip time is continuous: its interval model includes infinitely many possible values, including values between any two distinct times, rather than a countable list.
| Evidence for credit | Points |
|---|---|
| Correct classifications. | 1 |
| Distinguishes finite and countably infinite count sets. | 1 |
| Explains interval values between distinct times. | 1 |
Design a delivery data sheet: worked answer
A cooperative has 240 delivery trips in a week and samples 24 trips. For every selected trip it records driver ID (a numerical identifying code), distance in kilometres, number of stops, vehicle type, a photograph of the loaded vehicle, a 10-second audio clip, a video of unloading, and a driver comment. The sample mean distance is 18.5 km. For this exercise, an independently known full-week mean distance is 19.1 km.
Part a
Identify the observational unit and four variables, including at least one quantity and one category. Explain why the driver ID does not change the observational unit.
The unit is a delivery trip. Distance, stop count, vehicle type, and driver ID are possible variables. Distance and stop count are quantities; vehicle type and driver ID are categories/labels. One driver may have several trips, so recording an ID does not turn each trip row into a person row.
| Evidence for credit | Points |
|---|---|
| Trip unit and four variables. | 1 |
| Quantity/category distinction and repeated-driver reasoning. | 1 |
Part b
For each of photograph, audio, video, and text, propose one clearly defined piece of information that could be extracted.
Possible definitions are a photograph-based yes/no indicator of visible unsecured parcels; average audio noise level in decibels during the 10-second clip; a video count of parcels unloaded; and a comment category for the main delay (traffic, access, loading, other). Other reproducible, relevant coding rules are valid.
| Evidence for credit | Points |
|---|---|
| Meaningful defined information from each of four media. | 1 |
| Rules refer to the trip and can be applied consistently. | 1 |
Part c
Identify 18.5 km and 19.1 km as statistic or parameter. Explain their difference and the role the sample value could have if the full-week mean were unknown.
18.5 km summarizes 24 sampled trips and is a statistic. 19.1 km summarizes all 240 trips of interest and is the parameter. The sample happened to contain a different mix of trip distances. If the parameter were unknown, a properly selected sample statistic could help estimate it; it would not become the exact parameter.
| Evidence for credit | Points |
|---|---|
| Correct sample/population identification. | 1 |
| Explains discrepancy and possible inference without equating the values. | 1 |
Part d
Classify distance, stop count, vehicle type, and driver ID as categorical (qualitative) or quantitative (numerical). State the quantitative units. Explain why the numerical driver ID remains categorical despite being written with digits.
Distance is quantitative in kilometres and stop count is quantitative in stops. Vehicle type and driver ID are categorical. Driver IDs identify drivers, so numerical codes do not give a measured amount.
| Evidence for credit | Points |
|---|---|
| All four classifications and both quantitative units; accepts categorical/qualitative and quantitative/numerical synonyms. | 1 |
| Explains numerical identifier as label. | 1 |
Part e
Classify the underlying distance and stop count as continuous or discrete. Explain why rounding distance to 0.1 km does not turn the underlying quantity into a count.
Underlying distance is continuous under an interval model; stop count is discrete because possible values are whole numbers. Rounding restricts displayed records, but the underlying distance can still have values between two distinct recorded distances. It is a measured length, not a count of objects.
| Evidence for credit | Points |
|---|---|
| Correct two classifications. | 1 |
| Explains underlying interval values versus rounded record precision. | 1 |
Part f
Give a finite discrete trip variable and an idealized countably infinite discrete trip-related variable. Specify their possible values.
A yes/no delivery-success count for 12 parcels on a specified trip can be 0 through 12, a finite discrete set. An idealized count of attempts until the first successful delivery can be 1,2,3,… with no stated upper limit, a countably infinite discrete set. Equivalent clearly specified counts are valid.
| Evidence for credit | Points |
|---|---|
| Finite set and values stated. | 1 |
| Countably infinite whole-number set stated with no upper bound. | 1 |