7.7Statistics and Statistical Graphs

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

Warm-up

Homework Check

Statistics- numerical values used to summarize and

compare sets of data.

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.

x

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

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

Standard Deviation of a Data Set The standard deviation (read as “sigma”) of

x1, x2, …, xn is:

n

xxxxxx n22

22

1 )...()()(

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

= 36 34.2 + 39 34.2 + (40 - 34.2) + (34 - 34.2) + (48 - 34.2) + (33- 34.2) + (25- 34.2) + (30 - 34.2) + (37 - 34.2) + (17 - 34.2) + (42 - 34) + (40 - 34.2) + (24 - 34.2)

13

2 2 2 2 2 2 2 2 2 2 2 b g b g2 2

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, 34Median is 27.5

Upper: 37, 39, 40, 40, 42, 48 Median is 40

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.

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

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.

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.

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