1. Chapter 1
1.3 Describing Data
Math 10
Ms. Albarico

2. Students are expected to:
create and analyse plots using appropriate technology
solve problems using graphing technology
calculate various statistics using appropriate technology, analyse and interpret the displays, and describe the relationships
analyse statistical summaries, draw conclusions, and communicate results about distributions of data

3. Vocabulary Scattered(adj.) Distribute (v) Useful(adj.) Represent(v)
Compare(v)
Variations(n)
Varied(adj.)

4. What are the three common central tendencies?
Mean, Mode, Median
They are typical set of numbers called AVERAGE.

5. Mean
The mean is one kind of average. In order to calculate a mean, you would have to calculate the sum of your numbers and divide by the total number of elements in the set of numbers.

6. Median
The median is often described to be the middle value so it is also a kind of average. In order to find the median, you would have to put our numbers in either ascending (smallest to largest) or descending (largest to smallest) order. If there are an odd number of elements in the data set, the median is just the middle value. If there is an even number of elements in the data set; the median is the mean of the two middle values.

7. Mode
The mode of a data set is the value that occurs most often and is a third kind of average. A set could have no mode, one mode or two (bimodal) or more modes.

8. Outliers
Values that are significantly different from the majority of a set of data.

12. Practice Exercise
1. Find the mean, median, and mode for the following set of data.
(a) 2, 0, 0, 4, 3, 1, 2, 8, 2
(b) 10, 40, 10, 30, 10, 20, 30, 10, 10, 40
(c) 20, 27, 22, 21, 26, 25, 26, 22
2. Donna is reviewing her staff at the bank. She examines the list of tellers and determines the number of new RESP accounts they have opened during the past two months. She collected the following data:
Sandra Diego 23
Stephan 15 Curtis 7
Erica Janet 31
(a) Find the mean, median, and mode for this set of data.
(b) In a performance review of the tellers, how might the
median help Donna provide guidelines for future sales of
RESPs?

13. (b) What is his median salary?
Month
Pay
January $
February $
March $
April $
May $
June $
July $
August $
September $
October $
November $
December $
3. While filling out his income tax form, Dillon was going through his pay stubs for the previous year. He wrote down his pays for each month just to calculate his average monthly income. His list looked like the one below:
(a) What was the mean salary for Dillon during his previous year at his job?
(b) What is his median salary?
(c) What conclusions can you draw from looking at the chart?
(d) What is a better measure of his “average salary” - the mean or the median?
(e) Would the mode be useful here? Explain your thoughts.

16. Data Distribution

17. Stem-and-Leaf Plot

18. Organizes data in order of size
Key Terms:
Stem-and-leaf-plot - an organization of data into categories based on place value
Range – the difference between the least value and the greatest value in a set of data.
A stem-and-leaf plot
Organizes data in order of size
Can be used to find the range and all three measures of central tendency
Shows how data are distributed

19. Organize your data from Inv. 2 in increasing order.
Activity
Organize your data from Inv. 2 in increasing order.
Make a stem-and-leaf-plot from your data collected.

20. Box-and Whisker Plot
A type of graph used to display data. It shows how data are dispersed around a median, but does not show specific items in the data.
A box-and-whisker can also be used to display in order to see how they are distributed.

21. Box-and-whisker plot shows:
1) Lower Extreme – the least data value
2) Upper Extreme – the greatest data value
3) Lower Quartile – the median of the lower half of the data
4) Upper Quartile - the median of the upper half of the data
5) Mean
6) Median

22. Data

23. Steps in creating box-and-whisker plot:
Construct a number line and mark the lower and upper extremes, 12.1 and The difference between the extremes is the range of the data.

24. Steps in creating box-and-whisker plot:
Find the median of the data. Mark this value, 18.1, on the number line.

25. Steps in creating box-and-whisker plot:
Find the lower quartile. Mark this value on the number line. The median is found using the mean 16.5 and 17.1, which is 16.8.

26. Steps in creating box-and-whisker plot:
Find the upper quartile. Mark this value on the number line. The median is found using the mean 23.7 and 26.3, which is 25.0.

27. Steps in creating box-and-whisker plot:
Construct a box to show where the middle 50% of the data are located.

28. For Calculator Window:
Press Window
Xmin = 0
Xmax=50
Xscl=1
Ymin=0
Ymax=20
Yscl=1
Xres=1
In graphing box-and-whisker plot,
Xmin =Smallest value of x axis shown
Xmax =Greatest value of x axis shown
Xscl=scale of numbers of x axis shown
Ymin =Smallest value of y axis shown
Ymax =Greatest value of y axis shown
Yscl =scale of the numbers of y axis shown

29. For Calculator Window:
Make sure you know the least and greatest values of x and y coordinates.

30. Enter the data values in a list.
Using Calculator:
Enter the data values in a list.
Sort the data values.
Graph it.
Store your data values in a list.
Ex. L1
2nd Y=
Choose Stat Plots
1 ENTER
Choose Plot 1.
Press Enter to turn On.
 {5} ENTER
Move down to Type
Choose Type 5
Press ENTER
2nd 1
Enter List 1.
GRAPH
Press GRAPH.

31. Describing box-and-whisker plot:

32. Activity
1) Use 40 pieces data from Inv. 2 to construct a box-and-whisker plot. Check your work using graphing calculator.
Answer:
Compare the box-and-whisker plot and the stem-and-leaf plot.
Which is more effective display? Why?

33. Practice Exercise
Answer the hand out.

34. Homework(Notebook)
CYU # 13, 14, 16, &17
on pages

35. Frequency table Frequency Polygon Bar Graph
Histogram
Frequency table
Frequency Polygon
Bar Graph

36. What is a Frequency Table?
A Frequency table is a table that lists each item in a data set with the number of times it occurs.

37. Bar Graph

38. Construct a Frequency Table (tally sheet)
7, 10, 10, 9, 8, 9, 7, 4, 3, 7, 10, 4, 8, 9, 6, 7, 10
Enter the data value into the 1st column
Data Value
Tally
Frequency 1 2 3 4 5 6 7 8 9 10

39. Construct a Frequency Table (tally sheet)
7, 10, 10, 9, 8, 9, 7, 4, 3, 7, 10, 4, 8, 9, 6, 7, 10
Enter a tally for each entry.
Data Value
Tally
Frequency 1 2 3 4 5 6 7 8 9 10

40. Construct a Frequency Table (tally sheet)
Count the tallies and put the total for each value in the frequency column
Data Value
Tally
Frequency 1 2 3 4 5 6 7 8 9 10 1 2 1 4 2 3 4

41. What is a Histogram?
A histogram is a bar graph with no spaces between the bars.
The height of each bar shows the frequency of data within that interval.
The intervals of a histogram are of equal size and do not overlap.

42. A histogram
Is a graph used to display large sets of data by grouping the data into bins.
Shows how data are distributed.
In creating histogram, generally do not use more than 10 bins so that there are no more than 10 bars in the histogram. More than 10 bins makes the histogram difficult to read.

43. Histogram Histograms are used to show the frequency of data.
Very similar to bar graphs, but use intervals on the X axis.
Bars do touch.
Histograms have a title.
Histograms have two axes which are labeled.

44. Data

45. Creating Histogram

46. Creating Histogram

48. For Calculator Window:
Enter:
Xmin = 0
Xmax=50
Xscl=5
Ymin=0
Ymax=20
Yscl=1
Xres=1
In graphing histogram, Xscl is the
size of your bin, and
Ymax indicates the
frequency.

49. Enter the data values in a list.
Using Calculator:
Enter the data values in a list.
Sort the data values.
Graph it.
Store your data values in a list.
Ex. L3
2nd Y=
Choose Stat Plots
1 Enter
Choose Plot 1.
Press Enter to turn On. 
Choose Type 3
2nd 3
Enter List 1.
Graph
Press GRAPH.
Press TRACE to check the bin size and frequency.

50. Investigation 3 Perform Inv. 3. Write your report in an A4 paper.
Submit next meeting.

51. Practice Exercise
Answer the hand out.

52. Read about STANDARD DEVIATION. Download the notes from the website!
Homework (Notebook)
CYU # on page 25.
Read about STANDARD DEVIATION.
Download the notes from the website!