Try each one on paper first, then check a single step. That is worth far more than reading a finished solution.
Example 1 — all four measures from one data set
Find the mean, median, mode and range of 5,3,8,3,6.
- 1Mean =55+3+8+3+6=525=5Total divided by how many values there are.
- 2In order: 3,3,5,6,8Sort before doing anything with the median. This is where most marks are lost.
- 3Median =5Five values, so the middle one is the third.
- 4Mode =33 appears twice; everything else appears once.
- 5Range =8−3=5Largest minus smallest.
Example 2 — mean from a frequency table
Twenty students were asked how many siblings they have: 0 siblings (3 students), 1 (5 students), 2 (4 students), 3 (8 students). Find the mean.
- 1Multiply each value by its frequency.A value that occurs 8 times contributes 8 times over.
- 2∑fx=(0×3)+(1×5)+(2×4)+(3×8)
- 3=0+5+8+24=37This is the total number of siblings across all 20 students.
- 4∑f=3+5+4+8=20The total frequency — how many students there are.
- 5Mean =2037=1.85Divide by 20, not by 4. There are 20 pieces of data, not 4.
Example 3 — pie chart angles
Sixty students chose a sport: football 25, cricket 15, netball 12, athletics 8. Find the angle of each sector.
- 1Each angle is totalfrequency×360°The whole circle, 360°, represents all 60 students.
- 2Football: 6025×360=150°
- 3Cricket: 6015×360=90°A quarter of the students, so a quarter of the circle.
- 4Netball: 6012×360=72°
- 5Athletics: 608×360=48°
- 6Check: 150+90+72+48=360 ✓If the angles do not total 360°, one of them is wrong.