44
Data analysis
Textbook, pp. 203–205
GoalCalculate simple statistical measures: the mean, range, mode and median.
New words
mean (arithmetic average) · o‘rta arifmetikrange · o‘zgarish kengligimode · modamedian · mediana
Explanation
Four simple measures are used to analyse a list of numbers. The mean is the sum of all the numbers divided by how many there are. The range is the largest number minus the smallest. The mode is the number that occurs most often. The median is the middle number when the numbers are in increasing order; if there is an even count, it is the mean of the two middle numbers. How many times a number occurs is its absolute frequency; the mode is the number with the greatest frequency.
Worked examples
Marks 8, 6, 9, 7, 10: mean (8 + 6 + 9 + 7 + 10) : 5 = 8; range 10 − 6 = 4.
In 3, 5, 5, 2, 5, 3 the mode is 5 (it occurs 3 times). The median of 2, 4, 6, 10 is (4 + 6) : 2 = 5.
Class activity
“Class statistics”: pupils write down their shoe sizes and find the mean, mode, median and range. They discuss which measure is most useful for a shoe shop (the mode).
Practice
1
Find the mean of 4, 7, 10, 3, 6.
6
2
Find the range of 12, 5, 18, 9.
13
3
Find the median of 2, 9, 4, 7, 5.
5
4
Why must the numbers be put in order before finding the median?
The median is the middle number; in an unordered list the middle position means nothing.