A Level Math Revision Free diagnostic
Themed maths

Estimation station and class survey for A Level Maths

A first lesson that sets the tone: estimate first, then measure, and treat being wrong as part of maths. Then collect some anonymous class data and analyse it with the product-moment correlation coefficient, a regression line and a hypothesis test.

Level
A Level Maths (Year 12 and Year 13)
Time
40 minutes, plus a 10-minute extension
Topics
Statistical sampling and data: measures of location and spread; Correlation and regression; Hypothesis testing for correlation
Equipment
The starter is non-calculator. A calculator with statistics functions is needed.

Download student sheet (PDF)Answers (PDF)

Suggested timings

PartTimeWhat
Starter5 minQuick questions on the board
Main: task A10 minEstimation station
Main: task B15 minClass survey: correlation and regression
Main: task C10 minTravel times
Extension10 minFast finishers or homework

Starter (5 minutes)

Estimate, don’t calculate: round first.

  1. Estimate 3.982 × 25.1 by rounding each number to the nearest whole number.
  2. A student estimates that a corridor is 30 m long. It is really 24 m. Find the percentage error.
  3. Twelve estimates have Σx = 96. Find their mean.

Main activity (35 minutes)

Task A: Estimation station (10 min)

At each station, write your estimate first, then measure. These are one group’s results.

  1. Five estimates of the number of counters in a jar were 150, 210, 180, 260 and 200. Find the mean and the standard deviation (dividing by n).
  2. A corridor is 24 m long to the nearest metre and 2.5 m wide to the nearest 0.1 m. Find the upper bound of its floor area.

Task B: Class survey: correlation and regression (15 min)

Made-up data from eight students:

Height, h cm150155160165170175180185
Hand span, s cm1718182020212323

  1. Find the product-moment correlation coefficient, r.
  2. Find the equation of the regression line of s on h, and use it to estimate the hand span of a student 168 cm tall.
  3. Test, at the 5% level, whether there is positive correlation between height and hand span. The critical value for a sample of 8 (one-tailed, 5%) is 0.6215.

Task C: Travel times (10 min)

Made-up data: a class of 25 recorded how long their journey to school takes.

Time, t minutesFrequency
0 < t ≤ 106
10 < t ≤ 209
20 < t ≤ 307
30 < t ≤ 403

  1. Estimate the mean and the standard deviation.
  2. Use linear interpolation to estimate the median.

Extension (10 minutes)

For fast finishers.

  1. Every hand span in task B was measured 0.5 cm too short. Write down the corrected r and the corrected regression line.

For teachers

Teacher notes and full worked answers
  • Estimation station: set up four or five stations (a desk to measure, a jar of counters, a corridor, a book’s thickness, a minute with eyes closed). Students write an estimate first, then measure. Being wrong is the point: celebrate the closest estimate and the best reasoning, not just the right answer, and agree a class norm that a reasoned wrong answer is a good start.
  • Class survey: the data in the tasks are made up, so the answers can be checked. Then collect your own class’s anonymous data on the board (a show of hands for travel-time groups, hand spans written on sticky notes with no names) and repeat the calculations. Nothing is stored on the site.
  • Task B, question 3 is Year 13 content; with a Year 12 class, stop after the regression line and come back to it later.

Starter

  1. About 400
    • 42 × 25 = 400
  2. 25%
    • 6/24 × 100 = 25%
  3. 8
    • 96 ÷ 12 = 8

Task A: Estimation station

  1. Mean 200; standard deviation 36.3
    • Σx = 1000, Σx2 = 206 600
    • σ = √(206 600 ÷ 5 − 2002) = √1320 = 36.3
  2. 62.475 m2
    • 24.5 × 2.55 = 62.475

Task B: Class survey: correlation and regression

  1. r = 0.977
    • From the calculator: r = 0.97725…
  2. s = 0.181h − 10.3; 20.1 cm
    • s = 0.180952…h − 10.3095…
    • At h = 168: 20.09…
  3. Reject H0: there is evidence of positive correlation
    • H0: ρ = 0, H1: ρ > 0
    • 0.977 > 0.6215, so reject H0: there is evidence that taller students have wider hand spans.

Task C: Travel times

  1. Mean 17.8 minutes; standard deviation 9.6 minutes
    • Midpoints 5, 15, 25, 35
    • Mean = 445 ÷ 25 = 17.8
    • σ = √(409 − 17.82) = √92.16 = 9.6
  2. 17.2 minutes
    • The median is the 12.5th value, in 10 < t ≤ 20.
    • 10 + (12.5 − 6)/9 × 10 = 17.2

Extension

  1. r = 0.977 (unchanged); s = 0.181h − 9.81
    • Adding a constant to every s does not change r (coding).
    • The intercept goes up by 0.5: −10.3095… + 0.5 = −9.81

The same answers are in the answers PDF. Every answer was recomputed by computer before publishing.

Practise the topics

Prior-knowledge relay and maths bingo maths · Christmas escape room maths · Numbers round and word scramble maths · All themed maths

More for lessons: Weekly starters · Skill Builders · Worksheet builder · Competition maths