Measures of central tendency · Ages 14–15
Mean, median and mode
Sort first for the median; the mode comes most often.
How to do it
Method
Sort first for the median; the mode comes most often
3, 8, 5, 8, 6: mean 6, median 6, mode 8
Another way
An assumed mean
Differences −2, 3, 0, 3, 1 average 1, so 5 + 1 = 6
In full
Mean = the sum of the data ÷ how many there are. Median: put the data in order, smallest first; with an odd number take the middle one, with an even number the mean of the middle two. Mode: the value that comes most often. Take 3, 8, 5, 8, 6: the sum is 30, so the mean is 30 ÷ 5 = 6; in order, 3, 5, 6, 8, 8, the median is 6; 8 comes twice, so the mode is 8. With n data the median sits at place (n + 1) ÷ 2. From a frequency table, the mean is each value times its frequency, added, over the total frequency. Another way to the mean is an assumed mean: pick a number near the middle (say 5), find each value's difference from it, −2, 3, 0, 3, 1, whose mean is 5 ÷ 5 = 1, so the mean is 5 + 1 = 6; quicker with big numbers.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
A shoe shop sold seven pairs one day, in sizes 38, 35, 39, 37, 40, 36, 38. What is the mode of the sizes?
Show the answer and working
Answer: 38
The mode is the value that comes most often: 38 comes twice, every other value once.
Example 2
Five cars weigh 1157, 1163, 1161, 1154 and 1164 kg. What is their mean weight, in kg?
Show the answer and working
Answer: 1159.8 kg
The sum 5799 ÷ 5 = 1159.8. Or assume a mean: pick a number near them, average the differences from it, and add that back.
Example 3
A website gained 19, 12, 27, 9, 16, 14 new members on six days. The mean of these data is greater than the median.
True or false?
Show the answer and working
Answer: True
Mean = 97 ÷ 6 = 976; in order, the median is the mean of the 3rd and 4th, 15.
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.A basketball player scored 42, 26, 50, 33, 29 points in five games. How many points a game is that on average?
Answer:
2.The stem-and-leaf diagram shows the ages (in years) of a hiking group's members. What is the median age?
Answer:
3.The table shows how many bicycles each family on an estate owns (bicycles on the left, families on the right). How many bicycles does a family have on average?
Answer:
4.A cruise terminal had 39, 32, 44, 27, 37, 41, 31, 37 thousand passengers on eight days. The mean is , the median and the mode .
Fill in each blank
Answer:
5.A website gained 12, 8, 27, 6, 10, 9 new members on six days. The mean of these data is greater than the median.
True or false?
Answer:
All the answers
- 1. 36 points
- 2. 40 years
- 3. 3.95 bicycles
- 4. 36, 37, 37
- 5. True
VIP practice notes and papers
Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.
- Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
- Practice paper: Set out in parts like a school paper, marked, with answers and full working
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