Math Chapter 3 Data and Statistics
Notes
Mean, Median, Mode, Range –(should have definitions from 1 st
week of school)
A population is the entire group of people or objects that you want information about.
When it is difficult to survey an entire population, a sample is surveyed.
In a random sample, each person has an equally likely chance of being selected.
If persons are not selected randomly, it can result in a biased sample, which is not representative of the population.
A bar graph compares information and shows results in distinct categories. Example:
Title
100
80
60
40
20
0
1st Qtr 2nd Qtr 3rd Qtr 4th Qtr
Title
A line graph displays change over time . Example:
140
120
100
80
60
40
20
0 we ek
1 we ek
2 we ek
3 we ek
4
A stem-and-leaf plot is used to group data into ordered lists. Example: plant C plant B plant A
Title
3 5 7 9
4 0 2
 numbers are in order
 include all consecutive “stem” numbers even when there
6 1 1 4
7 9
A box-and-whiskers plot is used to display how the data are
 has a key
Key: 3| 5 = 35

A box-and-whiskers plot displays data beneath a number line.
1.
Start by finding the 5 “magic numbers”.
2.
Find the median , divide the numbers into two groups (upper and lower groups).
3. Find the median of each of these groups. ( upper quartile and lower quartile)
4. Finally, the largest and smallest numbers. ( upper extreme and lower extreme )
5. Plot these 5 numbers. Draw a box with a line down the middle using the middle three points. Then connect the upper and lower extreme points to the box using a straight line.
Example: 4, 5, 7, 9, 10, 12, 17, 20, 21,22 median: 11 , lower quartile: 7 , upper quartile: 20 , lower extreme: 4 , upper extreme: 22
3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
The points in the diagram are much larger than what you need to make on paper.
Interquartile range is the difference between the quartiles.
A histogram compares the frequencies of data that fall in equal intervals. To make a histogram, you must always first make a frequency chart .
Look at the set of numbers; determine an interval size that would produce between 3-8 intervals. Fill in the frequency chart accordingly; then make a graph that resembles a bar graph without any spaces between the bars.
Title of Graph
Interval Tally
1-3
4-6
7-9
IIII II
III
II
Frequency
7
3
2 n c u e y e q r f
6
5
4
3
7
2
1
10-12 IIII 5
1-3 4-6 7-9 10-12
intervals
Misleading displays can be made using a broken axis , large increments , or small intervals