CBSE Math Revision Start revising
Themed maths

Estimation station and class survey for CBSE Class 9 and 10

A first lesson of the session that sets the tone: estimate first, then measure, and treat being wrong as part of maths. Then collect some anonymous class data and find the mean, median and mode, all without a calculator.

Level
CBSE Class 9 and 10
Time
40 minutes, plus a 10-minute extension
Topics
Statistics: mean, median and mode of grouped data; Estimation and rounding; Statistics: averages and range
Equipment
No calculator. Every answer works out exactly.

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: travel times
Main: task C10 minHand spans
Extension10 minFast finishers or homework

Starter (5 minutes)

Estimate, don’t calculate: round first.

  1. Estimate 49.8 × 20.3 by rounding each number first.
  2. Estimate (612 + 389) ÷ 4.9.
  3. A student estimates that a corridor is 30 m long. It is really 24 m. By what percentage of the true length was the estimate out?

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. A student estimated that a desk is 90 cm long. It measured 120 cm. By what percentage of the true length was the estimate short?
  2. Five estimates of the number of beads in a jar were 150, 210, 180, 260 and 200. There are 196 beads. Find the mean of the estimates. How far is it from 196?
  3. Ten estimates of the length of the classroom, in metres, were 8, 9, 10, 10, 11, 12, 12, 12, 13, 13. Find the mode and the median.

Task B: Class survey: travel times (15 min)

Made-up data: 25 students recorded how long their journey to school takes.

Time (minutes)Number of students
0–106
10–209
20–307
30–403

  1. Find the mean journey time using the class marks.
  2. Find the median journey time.
  3. Find the mode of the journey times.

Task C: Hand spans (10 min)

Made-up hand spans (cm) of 10 students: 18, 20, 19, 22, 21, 17, 20, 23, 19, 21.

  1. Find the mean and the range.
  2. Find the median.

Extension (10 minutes)

For fast finishers.

  1. Two more students join the hand-span survey, with spans of 16 cm and 24 cm. Find the new mean and the new range.

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.
  • Tasks B and C use the Statistics chapter formulas for grouped data (Class 10) and the averages from Class 9.

Starter

  1. About 1000
    • 50 × 20 = 1000
  2. About 200
    • (600 + 400) ÷ 5 = 200
  3. 25%
    • 30 − 24 = 6
    • 6/24 × 100 = 25%

Task A: Estimation station

  1. 25%
    • 120 − 90 = 30
    • 30/120 × 100 = 25%
  2. Mean 200; 4 more than 196
    • Mean = 1000 ÷ 5 = 200
    • 200 − 196 = 4
  3. Mode 12 m; median 11.5 m
    • 12 appears three times.
    • The 5th and 6th values are 11 and 12: median = (11 + 12) ÷ 2 = 11.5

Task B: Class survey: travel times

  1. 17.8 minutes
    • Class marks 5, 15, 25, 35
    • Σfx = 30 + 135 + 175 + 105 = 445
    • Mean = 445 ÷ 25 = 17.8
  2. 155/9 = 17 2/9 minutes
    • n/2 = 12.5; cumulative frequencies 6, 15, 22, 25, so the median class is 10–20.
    • Median = l + ((n/2 − cf)/f) × h = 10 + (12.5 − 6)/9 × 10 = 10 + 65/9 = 155/9
  3. 16 minutes
    • The modal class is 10–20 (frequency 9).
    • Mode = l + ((f1 − f0)/(2f1 − f0 − f2)) × h = 10 + (9 − 6)/(18 − 6 − 7) × 10 = 10 + 6 = 16

Task C: Hand spans

  1. Mean 20 cm; range 6 cm
    • Total 200, so mean = 20
    • 23 − 17 = 6
  2. 20 cm
    • In order: 17, 18, 19, 19, 20, 20, 21, 21, 22, 23
    • (20 + 20) ÷ 2 = 20

Extension

  1. Mean 20 cm; range 8 cm
    • (200 + 16 + 24) ÷ 12 = 240 ÷ 12 = 20
    • 24 − 16 = 8

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 · Olympiad and competition maths · National Mathematics Day puzzles