CBSE Math Revision Start revising
Themed maths

Big tournament statistics for CBSE Class 10

A ready-to-teach statistics lesson built on a made-up tournament: a 5-minute starter, a 35-minute main activity on goals per match, batting scores as grouped data and probability, an extension and full worked answers. No calculator. All the data are made up for this lesson.

Level
CBSE Class 10
Time
40 minutes, plus a 10-minute extension
Topics
Statistics: mean, median and mode of grouped data; The empirical relationship between mean, median and mode; Probability
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 A11 minGoals per match
Main: task B13 minBatting scores
Main: task C11 minChance
Extension10 minFast finishers or homework

Starter (5 minutes)

Quick-fire mental maths.

  1. Find the mean of 2, 4, 4, 5, 10.
  2. Find the median of 3, 8, 1, 9, 4, 7.
  3. Find the mode of 2, 3, 3, 5, 7, 3.
  4. Two dice are thrown. Find the probability of a double.

Main activity (35 minutes)

Task A: Goals per match (11 min)

Made-up goals in 40 matches: 0 goals in 4 matches, 1 in 9, 2 in 11, 3 in 8, 4 in 5, 5 in 2 and 6 in 1.

  1. Find the mean number of goals per match.
  2. Find the median number of goals.
  3. Find the mode.

Task B: Batting scores (13 min)

Made-up runs scored by 40 batters: 0–20: 5, 20–40: 8, 40–60: 12, 60–80: 10, 80–100: 5.

  1. Find the mean score using the step-deviation method.
  2. Find the median score.
  3. Find the mode, and check the empirical relation 3 median = mode + 2 mean.

Task C: Chance (11 min)

Use the data above.

  1. A match is chosen at random from the 40. Find the probability that it had 3 or more goals.
  2. A batter is chosen at random. Find the probability that they scored 60 or more.
  3. Find the probability that a match chosen at random had no goals.

Extension (10 minutes)

For fast finishers, or as homework.

  1. After 8 more matches, the mean number of goals over all 48 matches is 2.5. How many goals were scored in those 8 matches?
  2. In the batting table, the frequency of the 80–100 class is changed from 5 to f, and the mean becomes 58.8. Find f.

For teachers

Teacher notes and full worked answers
  • Every number in this pack is made up for the lesson; say so when you show it.
  • Task B covers all three grouped-data formulas from the Statistics chapter; the step-deviation method keeps the arithmetic small.
  • In task B (b), the common slip is using the cumulative frequency of the median class instead of the class before it.

Starter

  1. 5
    • 25 ÷ 5 = 5
  2. 5.5
    • 1, 3, 4, 7, 8, 9: (4 + 7)/2 = 5.5
  3. 3
    • 3 occurs three times.
  4. 1/6
    • 6 doubles out of 36 outcomes.

Task A: Goals per match

  1. 2.275
    • Σfx = 0 + 9 + 22 + 24 + 20 + 10 + 6 = 91; Σf = 40.
    • 91/40 = 2.275
  2. 2
    • n = 40: the 20th and 21st values. Cumulative frequencies 4, 13, 24, … so both are 2.
  3. 2
    • 2 goals has the highest frequency, 11.

Task B: Batting scores

  1. 51
    • Class marks 10, 30, 50, 70, 90; take a = 50, h = 20, so u = −2, −1, 0, 1, 2.
    • Σfu = −10 − 8 + 0 + 10 + 10 = 2; mean = 50 + 20 × 2/40 = 51
  2. 155/3 = 51 2/3
    • n/2 = 20. Cumulative frequencies 5, 13, 25, …, so the median class is 40–60.
    • Median = 40 + (20 − 13)/12 × 20 = 40 + 35/3 = 155/3
  3. 160/3 = 53 1/3; 155 ≈ 53 1/3 + 102 = 155 1/3
    • Modal class 40–60: mode = 40 + (12 − 8)/(2 × 12 − 8 − 10) × 20 = 40 + 40/3 = 160/3.
    • 3 × 155/3 = 155 and 160/3 + 2 × 51 = 155 1/3: very close.

Task C: Chance

  1. 2/5
    • 8 + 5 + 2 + 1 = 16; 16/40 = 2/5
  2. 3/8
    • 10 + 5 = 15; 15/40 = 3/8
  3. 1/10
    • 4/40 = 1/10

Extension

  1. 29
    • 48 × 2.5 = 120; 120 − 91 = 29
  2. 15
    • Σfx = 50 + 240 + 600 + 700 + 90f = 1590 + 90f and Σf = 35 + f.
    • 1590 + 90f = 58.8(35 + f) = 2058 + 58.8f, so 31.2f = 468 and f = 15.

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

Practise the topics

Eclipse geometry maths · Ada Lovelace Day maths · Halloween maths · All themed maths

More for lessons: Weekly starters · Worksheet builder · Olympiad and competition maths · National Mathematics Day puzzles