warm-up marina has the following quiz grades in her discrete math class: 84, 90, 96, 100, 67, 88,...
TRANSCRIPT
WARM-UP
Marina has the following quiz grades in her Discrete Math class:
84, 90, 96, 100, 67, 88, 90, 92, 94.
Find the mean, median, mode, and standard deviation for Marina’s quiz grades.Mean=89 Median=90 Mode=90SD=8.92
Histograms, Stem & Leaf, Box & Whiskers
Day 2
Steam and Leaf Plot Method of arranging data in increasing or decreasing
order
“Stem” – left side of column which contains the tens digits
“Leaf” – right side of column which contains the ones digits
Must have a key
Example 1 – Data for Ages of People Online After Midnight
18 45 67 1920 35 72 2268 27 34 3519 21 24 3261 55 24 25
We want to use this data to create a stem and leaf plot
Ex 1 cont. - Stem & Leaf Plot
1
2
3
4
5
6
7
18 4567 19
20 3572 22
68 2734 35
19 2124 32
61 5524 25
Stem
8 9 9
0 1 2 4 4 5 7
2 4 5 5
2
5
1 7 8
5
Leaf
Ex 2: Steam and Leaf PlotCreate a steam and leaf plot with these values:7.6 8.1 9.2 6.8 5.9 6.2 6.1 5.8 7.3 8.1 7.4 8.8 7.7 8.2
5
6
7
8
9
**Steam & Leaf plots make no accommodations for decimals
**ones digits = steam and tenths = leaf
8 9
1 2 8
3 4 6 7
1 1 2 8
2
You Try!!!Create a steam and leaf plot with these recent test scores:
73 42 67 78 99 84 91 82 86 94
4
5
6
7
8
9
2
7
3 8
2 4 6
1 4 9
Histogram Variation of a bar graph to arrange data Used for continuous variable We must use frequency tables to organize data
before creating a histogram Must decide class intervals for data:
Deciding data into reasonable increments Grouping data together
Class intervals: Must be equal length Columns must touch because there aren’t any gaps between
class intervals Value that falls on boundary between class intervals
is called endpoint convention
How to make a Frequency Table
Separate data into a range and counts the frequency (%) for each range.
Class Interval Width=
Relative Frequency=
edervalswantof
elowestvaluuehighestval
int#
datapts
frequency
#
Example 1 – Data for Ages of People Online After Midnight
18 45 67 1920 35 72 2268 27 34 3519 21 24 3261 55 24 25
We want to use this data to create a frequency table in order to draw a histogram
There are 20 total data points therefore 5 intervals would make data reasonable to work with.
Find interval width = 118.105
54
5
1872
Frequency TableInterval Frequency
(# data points in class interval)
Relative Frequency
USE THIS TO DRAW A HISTOGRAM!!!
20 data points
5 class intervals with length of 11
17 - 28
28 - 39
39 - 50
50 - 61
61 - 72
10
4
1
2
3
50%
20%
5%
10%
15%
datapts
frequency
#
Ages
Histogram
Box & Whiskers Plot
Method of displaying data that uses quartiles (separate data) to form the center box
Whiskers – minimum & maximum values
Steps to Create Box and Whiskers Plot
1) Order the data to find the median value
2) Divide the data into 2 parts using the median
1st part of data – to the left of the median value 2nd part of data – to the right of the median value
3) Find the median of each half of the data
4) Label the medians, minimum, maximum values of the data to draw the box and whiskers plot
Ex 1: Box and Whiskers Plot
Make box and whiskers plot for these values
91 95 88 85 90 97 94 100 81
1) Order the data:
81 85 88 90 91 94 95 97 100
2) Label the data
3) Find the median of the first half of data and the second half of data
4) Draw Box and Whiskers Plot
Minimum MaximumMedianMedian=86.5 Median=96
Ex 2: Box and Whiskers Plot
Make box and whiskers plot for these values
84 79 90 73 95 88 92 81 67
1) Order the data:
67 73 79 81 84 88 90 92 95
2) Label the data
3) Find the median of the first half of data and the second half of data
4) Draw Box and Whiskers Plot
Minimum MaximumMedianMedian=76 Median=91
You Try!!!
Create a Box and Whiskers plot for these values
34 36 47 45 28 31 29 40
28 29 31 34 36 40 45 47Minimum Maximum
Median=35Median=30 Median=42.5