Chapter 1 1.3 Describing Data Math 10 Ms. Albarico

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

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

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

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.

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.

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.

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

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 12 Diego 23 Stephan 15 Curtis 7 Erica 9 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?

(b) What is his median salary? Month Pay January $ 275.23 February $ 250.45 March $ 223.50 April $ 295.23 May $ 322.34 June $ 175.95 July $ 675.76 August $ 715.78 September $ 375.02 October $ 267.87 November $ 254.56 December $ 432.42 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.

Data Distribution

Stem-and-Leaf Plot

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

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.

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.

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

Data

Steps in creating box-and-whisker plot: Construct a number line and mark the lower and upper extremes, 12.1 and 12.86. The difference between the extremes is the range of the data.

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

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.

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.

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

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

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

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.

Describing box-and-whisker plot:

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?

Practice Exercise Answer the hand out.

Homework(Notebook) CYU # 13, 14, 16, &17 on pages 20-21.

Frequency table Frequency Polygon Bar Graph Histogram Frequency table Frequency Polygon Bar Graph

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.

Bar Graph

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

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

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

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.

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.

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.

Data

Creating Histogram

Creating Histogram

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.

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.

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

Practice Exercise Answer the hand out.

Read about STANDARD DEVIATION. Download the notes from the website! Homework (Notebook) CYU # 26-29 on page 25. Read about STANDARD DEVIATION. Download the notes from the website! www.ilovemathisfun.com