10.1 Stem-and-Leaf Plots
A way to show data, the stem is the upper half/other number's and the leaf is the ones place.
What is a Stem-and-Leaf Plot?
A bar graph that shows the frequency of data values in intervals of the same size.
What is a Histogram?
Describes the spread of data, can be skewed left, skewed right, or symmetric.
What are Shapes of Distribution?
Symetric:Mean and MAD
Skewed: Median and IQR
What are the appropriate measures for the corresponding distributions: Symetric and Skewed
Represents a data set along a number line by using the least value, greatest value, and quartiles.
What is a Box-and-Whisker Plot?
A stem-and-leaf plot of the following data.
Books read:
26, 15, 20, 9, 31, 25, 29, 32, 17, 26, 19, 40
What is
Stem____lLeaf_______
0 l 9
1 l 5 7 9
2 l 0 5 6 6 9
3 l 1 2
4 l 0
Key:4/0=40 books read
The peak.
Chess Team Wins Frequency
10-13 3
14-17 5
18-21 4
22-25 2
What is 5?
The left and right sides of the graph mirror each other.
Describe symmetric.
The appropriate measures for skewed left.
What are the IQR and median?
The five number summary.
What is the five that make up the box-and-whisker plot?
What are the least value, greatest value, median, 1st quartile, and 3rd quartile?
A stem-and-leaf plot of the data.
Minutes in Line:
4.0, 2.6, 1.9, 3.1, 3.6, 2.2, 2.7, 3.8, 1.6, 2.0, 3.1, 2.9
What is
_Stem_l_Leaf__
1 l 6 9
2 l 0 2 6 7 9
3 l 1 1 6 8
4 l 0
Key: 3/1=3.1 mins in line
Key:
The gap in a histogram of the following data.
minutes watched frequency
15-25 5
26-36 8
37-47 0
48-58 7
What is the section of 37-47 with 0.
Most of the data is on the left and the tail is on the right.
Describe skewed right.
The appropriate measures for Symmetrical.
What are the mean and MAD?
The measurments that make up the box-and-whisker plot with this data. (ages of teachers)
30, 62, 26, 35, 45, 22, 49, 32, 28, 50, 42, 35
least-22
greatest-62
Q1-29
Q2-35
Q3-47
Error analysis:
The error in the stem-and-leaf plot of following data.
51, 25, 47, 42, 55, 26, 50, 44, 55
Wrong way:
__Stem___l___Leaf___
2 l 5 6
4 l 2 4 7
5 l 0 1 5 5
Key: 4/2=42
What is the 3 stem?
In making a stem-and-leaf plot you have to have all the numbers in the stem, even if there is no leaf there.
So this one is missing the three, in 2 4 5.
____Stem__l__Leaf_____
2 l 5 6
3 l
4 l 2 4 7
5 l 0 1 5 5
The total number of students that read magazines from this data.
Magazines read Frequency
1-3 6
4-6 7
7-9 3
10-12 1
What is 17?
The Frequency is how many people read it, so you just add all those together.
The distribution of the following data. (dot plot)
1, 4, 2, 0, 3, 2, 1, 2, 4, 2, 3, 2, 1, 6, 3, 2, 4, 0, 5, 3, 1, 5
Skewed left.
The IQR and median for the left skewed data.
6, 7, 8, 9, 9, 10, 10, 11, 11, 11, 12, 12, 12, 12, 12, 13, 13, 13, 14
What is 11 and 3?
The fraction of teachers that are older than 30 and the IQR of the ages.
(From last problem in this section, 300)
What is 3/4 and 18?
Each stem-and-leaf plot below has a mean of 39. One has the lesser mean absolute deviation (MAD) without needing to calculate the exact MAD.
Explain your reasoning.
#1 #2
____stem_l____leaf___ ____Stem_l___leaf__
2 l 3 7 2 l 2 4 5 8 9
3 l 0 2 6 9 3 l 3
4 l 1 2 5 8 4 l 5
5 l 1 4 5 l 3 6 7 8
Key: 4/1=41 Key: 5/3=53
What is Stem-and-Leaf Plot #1?
The MAD means an average how far the rest of the numbers differ from the mean. You want the lowest MAD. So, if there are more numbers that are closer/are the mean, the less they differ (lower Mad) So you want the plot with the #'s that are closest to 39, which, #1 has more that is the 30's, so that one would have the lower MAD. Plus #2 has more in the 50's, the most farthest away tens.
The percent of the data that took more that 5-9 minutes to download.
Mins to download Frequency
1-4 9
5-9 6
10-14 2
15-19 3
What is 0.25%?
The distribution of the following data.
15, 12, 16, 15, 13, 14, 16, 13, 13, 16, 14, 12, 15, 12, 14
Symmetric!!
The MAD and mean of the symmetric data.
8, 10, 10, 12, 12, 12, 14, 14, 14, 14, 16, 16, 16, 18, 18, 20
What is 14 and 2.5?
The one with more varibility.
The teachers that are older than 47.
The teachers younger than 29.
(From the previous question in the 300 zone)
What is the group of teachers that are older than 47?
The whisker of this group is longer which means there is more options of ages within that range. The difference of the oldest age, 62, and Q3, 47, is 15. This is bigger than the other whisker.