Mean, median, mode and range GCSE lesson: lists, frequency tables, which average

Averages: practice

Show your working on paper: order the data first. The stretch is optional.

Diagnostic question: choose and explain

1. Shoe sizes of 20 people: size 4: 2 people, size 5: 5 people, size 6: 8 people, size 7: 5 people. What is the mean shoe size?
   1. 5
   2. 5.8
   3. 29
   4. 5.5

Practice questions

1. Find the mean of 4, 9, 2, 7 and 8.
2. Find the median of 14, 3, 8, 19, 6 and 10. Then drag the marker to it on the number line.They drag a marker on a number line from 0 to 20.
3. Brothers and sisters of 25 students: 0: 5 students, 1: 9 students, 2: 7 students, 3: 3 students, 4: 1 student. What is the mode?
   1. 2
   2. 9
   3. 1
   4. 4
4. The same 25 students: 0: 5 students, 1: 9 students, 2: 7 students, 3: 3 students, 4: 1 student. Find the mean number of brothers and sisters.
5. The mean of 7, 9, x, 4 and 10 is 8. Solve the equation for x, one line at a time.They solve (7 + 9 + x + 4 + 10)/5 = 8 line by line, each line checked as they write it.
6. Which average would you choose for each set of data? Sort each one into its group.They sort 6 items into Mean and Median and Mode.
7. In a quiz, team A's scores had a mean of 62 and a range of 30. Team B's had a mean of 58 and a range of 12. Which is the best comparison?
   1. Team A scored more on average; team B's scores were more consistent
   2. Team A is better, because 62 is more than 58
   3. Team B scored more on average, because its range is smaller
   4. Team A's scores were more consistent, because its range is bigger
8. The mean of six numbers is 7. A seventh number is added, and the mean of all seven is 8. What is the seventh number?
9. Stretch: journey times of 20 students. 0 < t ≤ 10 minutes: 4 students; 10 < t ≤ 20: 10 students; 20 < t ≤ 30: 6 students. Estimate the mean time in minutes.

Support: For a table: write one row out as a list (size 5, five times: 5, 5, 5, 5, 5). The total for that row is 5 × 5. Add every row's total, then divide by the number of people.

Averages: exit

Place the mean, then one or two sentences.

1. Five values: 2, 3, 3, 8 and 9. Drag the marker to their mean on the number line.They drag a marker on a number line from 0 to 10.
2. For 2, 3, 3, 8 and 9, the median is 3. Which would you give as the typical value, the mean or the median? Say why in a sentence or two.

Exit check

Place a mean on a number line, then say which average is typical.

Place the mean of 2, 3, 3, 8 and 9 on the number line.

Averages: lists, tables and choosing

Order the data first, and show your working. For a table, divide by the total frequency. Answer questions 4 and 5 in full sentences.