1. 7.7 Statistics and Statistical Graphs

2. Learning Targets  Students should be able to… Use measures of central tendency and measures of dispersion to describe data sets. Use box-and-whisker plots and histograms to represent data graphically

3. Warm-up 

4. Homework Check

5. Statistics-  numerical values used to summarize and compare sets of data.

6. Measures of central tendency Mean or average: add all of your data and divide by the number of data you have. (denoted ) Median: the middle number when the numbers are in order from smallest to largest. Mode: the number or numbers that appear most frequently.

7. 1. Be able to find the mean, median and mode and measures of dispersion. Example 1: The number of games won in the Eastern Conference for the 1987-1998 regular season of the National Hockey League is shown in the chart below. Eastern Conference 36, 39, 40, 34, 48, 33, 25, 30, 37, 17, 42, 40, 24 Mean= (36+39+40+34+48+33+25+30+37+17+42+40+24)/13= 34.23 Median: Reorder:17, 24, 25, 30, 33, 34, 36, 37, 39, 40, 40, 42, 48 Median is 36 Mode is 40

8. Range:  the difference between the greatest and the least data value.  Find the range of the number of wins in the data set from example 1 48 – 17 = 31

9. Standard Deviation of a Data Set  The standard deviation  (read as “sigma”) of x 1, x 2, …, x n is:

10. Example 2:  Find the standard deviation for the number of wins. Eastern Conference 36, 39, 40, 34, 48, 33, 25, 30, 37, 17, 42, 40, 24

11.  Lower quartile: the median of the lower half  Upper quartile: the median of the upper half. Eastern Conference 36, 39, 40, 34, 48, 33, 25, 30, 37, 17, 42, 40, 24 Find the upper and lower quartile for the data set. Lower: 17, 24, 25, 30, 33, 34 Median is 27.5 Upper: 37, 39, 40, 40, 42, 48Median is 40

12. 2. Be able to construct a box-and- whisker plot. 1. Order the data from least to greatest. 2. Find the minimum and maximum values. 3. Find the median. 4. Find the lower and upper quartiles. 5. Plot these five numbers below a number line. 6. Draw the box, the whisker, and a line segment through the median.

13. Example 3: Draw a box and whisker plot for the data from example 1. Eastern Conference 36, 39, 40, 34, 48, 33, 25, 30, 37, 17, 42, 40, 24

14. 3. Be able to construct a histogram and frequency distribution.  Histogram: a special type of bar graph.  Frequency: The number of data values in each interval.  Frequency distribution- a chart that shows the frequency of each interval.  Note: It is helpful to construct a frequency distribution before you construct your histogram.

15. Example 4: a) Make a frequency distribution for the data set in example 1. Use four intervals beginning with the interval 11 – 20. Eastern Conference 36, 39, 40, 34, 48, 33, 25, 30, 37, 17, 42, 40, 24 b) Draw a histogram for each data set in our frequency distribution.

16. Bringing it all together! Example:  Find the standard deviation, mean median and mode for the following test scores  92, 94, 87, 76, 69, 82, 62, 90, 76, 82, 85, 87, 64, 61, 95, 87  Draw a histogram (Use intervals starting at 60 – 64)  Draw a box and whisker plot