Measures of centre in context · Grade 10 · 3 units
In Measures of centre in context (Grade 10 · 3 units) you practise 3 skills: The measure that fits · A measure after a change · Deciding with a statistic and a chance. The mean, the median and the mode are three measures of centre, and each answers a different question. The mean is the sum divided by how many values there are, and it fits sharing out equally. The median is the middle value when the data are in order, and it fits when there is an extreme value. The mode is the value that appears most often, and it fits when you want to know what is most common.
When a value joins or leaves, work out the sum and the count again. When the same number is added to every value, the mean and the median both go up by that number. To find the mean of two groups together, add the groups’ totals and divide by the number of all the values. To decide between two options, compare the same measure in both. The probability that a value picked at random fits a condition is the number of values that fit divided by the number of all the values.
Tip: One very large value pulls the mean, but hardly moves the median.
What you learn
The measure that fits
For example: The monthly salaries of six workers at a company, in thousands: 11, 44, 13, 14, 14, 9 Which measure best describes a typical salary at the company?
- The mean
- The mode
- The median
Answer and solution
The answer: The median
One salary, 44 , is far above the rest and pulls the mean up. The median is not affected by it, so it describes a typical salary.
A measure after a change
For example: These are a student’s test scores so far: 72, 58, 93, 100, 71, 65 In the next test the student scored 52 . What is the mean of all the scores now?
Answer and solution
The answer: 73
The new sum: 72 + 58 + 93 + 100 + 71 + 65 + 52 = 511 , and there are now 7 scores. The mean: 511 ÷ 7 = 73
Deciding with a statistic and a chance
For example: These are the scores of five players from each team in a game. The red team: 56, 98, 57, 74, 95 . The blue team: 87, 59, 58, 51, 88 . Which team has the higher mean?
- The blue team
- The red team
Answer and solution
The answer: The red team
The red team: (56 + 98 + 57 + 74 + 95) ÷ 5 = 76 . The blue team: (87 + 59 + 58 + 51 + 88) ÷ 5 = 68.6 .
Not on the site yet
Parts of this topic that are not built yet: Explaining the choice of a measure in words · Planning a survey and collecting data.
The exercises are made by rules and the answers are worked out in code, so there are new exercises every time. The topic follows the Israeli Ministry of Education’s high school maths curriculum at 3 units (grades 10 and 11).