69
A data set and its analysis
Textbook: Part 2, lesson 69, pp. 134–136
GoalData series and analysis: range, mean, median and mode.
New words
range · o‘zgarish oralig‘imedian · medianamode · modadata series · ma’lumotlar qatori
Explanation
To analyse a data series we use four measures. The range is the difference between the largest and the smallest numbers; it shows how spread out the data are. The mean is the sum divided by the number of values. The median is the middle number of the series written in increasing order; if the count is even, take the mean of the two middle numbers. The mode is the number that occurs most often; a series may have no mode or two modes. For example, a school canteen cooks more of the dish that is ordered most often (the mode).
Worked examples
Series: 4, 7, 4, 9, 6. In order: 4, 4, 6, 7, 9. Range 9 − 4 = 5; median 6; mode 4 (twice); mean (4 + 7 + 4 + 9 + 6) : 5 = 6.
Series: 2, 5, 5, 8, 10, 12 (6 numbers). Median (5 + 8) : 2 = 6.5; mode 5; range 12 − 2 = 10; mean 42 : 6 = 7.
Class activity
“Class statistics”: ask classmates how many brothers and sisters they have, make a series of 8–10 numbers, put it in increasing order and find the range, median and mode.
Practice
1
Find the range of the series 12, 9, 15, 9, 20.
11
2
Find the median of the same series.
12
3
Find the median of the series 3, 8, 1, 6.
4.5
4
When does a series have no mode?
When all numbers occur the same number of times (for example, once each).