Time Series, Moving Averages and Quality Assurance
How do you see the real trend when data jumps up and down with the seasons? Learn to smooth a time series with moving averages, and how factories use control charts to keep quality on track.
Revise this, the fun way
Play it interactively, earn XP and build a streak, free.
Start revising freeWhat you'll cover
Data over time 📈
A **time series** is data recorded at **regular intervals over time** - monthly sales, daily temperatures, quarterly profits - and plotted as a line graph. Two features matter: the **trend** (the general long-term direction - rising, falling or flat) and **seasonal variation** (regular ups and downs that repeat, like ice cream sales peaking each summer). The problem: the seasonal jumps can hide the trend. This module shows how a **moving average** fixes that, and how factories use the same statistics for **quality control**.
Words for a time series 🗂️
Learn these four - the steps that follow put them to work.
Match each term to its meaning 🔗
- Time series
- Trend
- Seasonal variation
- Moving average
- Data collected at regular intervals over time
- The general long-term direction of the data
- A regular up-and-down pattern that repeats each period
- An average of consecutive values, repeated to smooth the data
Read the trend 📉
A shop's quarterly sales rise every summer and fall every winter, but each year's figures are a little higher than the last. What is the underlying trend?
- Rising - the overall level increases year on year despite the seasonal ups and downs
- Falling - because sales drop every winter
- Flat - the seasons cancel out to nothing
- There is no trend, only seasonal variation
Calculate a moving average ➗
An interactive activity.
How the smoothing works 〰️
A **4-point moving average** takes four values in a row, averages them, then slides along one step and does it again - so with quarterly data each average covers a whole year. Because every average includes one of each season, the seasonal highs and lows **cancel out**. Plotting the moving averages gives a much **smoother line** that shows the real **trend**. (The general version averages any n points: (x1 + ... + xn) / n. [Higher])
Why use a moving average? 🔍
What is the main reason for calculating a moving average of a time series?
- To smooth out the seasonal variation so the underlying trend is clear
- To make all the numbers bigger
- To find the most common value in the data
- To measure how spread out the data is
Quality control lines [Higher] ⚖️
Factories check quality by taking samples and plotting each SAMPLE MEAN on a control chart. (Sample means are less spread out than individual items.) Two pairs of lines sit either side of the target.
Match each situation to the response [Higher] 🚦
- Sample mean within all the lines
- Sample mean outside a warning line
- Sample mean outside an action line
- The process is running normally; carry on
- Take another sample and watch closely; it may be chance
- Stop production and investigate or adjust the process
Quality assurance facts [Higher] ✅
Select the TWO statements that are correct about quality-assurance control charts.
- Sample means are more closely distributed than individual measurements
- Action lines are drawn at plus or minus 3 standard deviations
- A point outside a warning line means production must stop at once
- A point outside an action line can safely be ignored
Smooth a time series, in order 🪜
An interactive activity.
On the factory floor 🧭
An interactive activity.
Your turn ✍️
An interactive activity.
The grade-9 habit 🌟
Two things win marks here. First, always say **why** a moving average is used: it **smooths the seasonal variation** so the **trend** shows - not to change the numbers. Second, be careful with prediction. Extending a trend a little way can be reasonable, but **extrapolating** far beyond the data is risky because the trend may not hold [Higher]. And for quality assurance, remember the pair: a **warning** line (+/-2 SD) means **re-sample**, an **action** line (+/-3 SD) means **stop and investigate** [Higher]. Naming the response is the mark-winner.