59
Final review: data
Textbook, p. 233
GoalReview tables, diagrams, statistical measures and combinatorics.
New words
mean · o‘rta arifmetikmode · modamedian · medianamultiplication rule · ko‘paytirish qoidasi
Explanation
We present data with tables and diagrams: a bar chart compares values, a line graph shows change, a pie chart shows the parts of a whole (the whole circle is 360° and a p% sector is 360° · p : 100). For a list of numbers: the mean is sum : count; the range is largest − smallest; the mode is the number occurring most often; the median is the middle of the ordered list. In combinatorics, ways add (m + n) in “either-or” situations and multiply (m · n) in “both ... and” situations.
Worked examples
12, 15, 11, 15, 17, 15, 13: sum 98, count 7, mean 14; range 17 − 11 = 6; mode 15; ordered list 11, 12, 13, 15, 15, 15, 17 gives median 15.
A menu has 3 soups and 4 main dishes. A lunch (soup and main dish) can be chosen in 3 · 4 = 12 ways; choosing just one dish gives 3 + 4 = 7 ways.
Class activity
“Data collectors”: the class collects data on daily hours of sleep, makes a table and a diagram and calculates the mean and the mode. Groups write one conclusion from the results.
Practice
1
Find the mean of 12, 15, 11, 15, 17, 15, 13.
14
2
Find the range of the same list.
6
3
How many lunches can be made from 3 soups and 4 main dishes?
12
4
Which measure is more useful for a shoe shop, the mean or the mode? Why?
The mode: it shows the most commonly needed size. The mean may not match any real size.