a.
To Create: The stemplot of the length of songs.
The stemplot is:
Stem | Leaf |
12 | 0 0 4 4 |
13 | 1 1 2 6 7 9 |
14 | 0 3 4 8 |
15 | 6 |
16 | 3 |
17 | 7 9 |
18 | 0 |
19 | 0 1 7 |
20 | 2 |
23 | 0 |
Given:
The length (in seconds) of the songs is as follows:
Length |
120 |
120 |
124 |
124 |
131 |
131 |
132 |
136 |
137 |
139 |
140 |
143 |
144 |
148 |
156 |
163 |
177 |
179 |
180 |
190 |
191 |
197 |
202 |
230 |
Plot:
Arrange the data in ascending order and consider the first two digits of the data as stem.
The last digit of each data value is placed in leaf.
The stemplot is obtained as:
Stem | Leaf |
12 | 0 0 4 4 |
13 | 1 1 2 6 7 9 |
14 | 0 3 4 8 |
15 | 6 |
16 | 3 |
17 | 7 9 |
18 | 0 |
19 | 0 1 7 |
20 | 2 |
23 | 0 |
b.
The shape of the distribution.
The shape of the distribution of the data is not symmetrical.
Given:
The length (in seconds) of the songs is as follows:
Length |
120 |
120 |
124 |
124 |
131 |
131 |
132 |
136 |
137 |
139 |
140 |
143 |
144 |
148 |
156 |
163 |
177 |
179 |
180 |
190 |
191 |
197 |
202 |
230 |
The stemplot is obtained as:
Stem | Leaf |
12 | 0 0 4 4 |
13 | 1 1 2 6 7 9 |
14 | 0 3 4 8 |
15 | 6 |
16 | 3 |
17 | 7 9 |
18 | 0 |
19 | 0 1 7 |
20 | 2 |
23 | 0 |
Explanation:
From the stemplot, it can be observed that data has peak at stem 12.
If the spread of data at first peak is considered from stem 12 to 15, it can be observed that the upper part of data is skewed to right and not symmetric.
The lower part of the data from stem 16 to 23 does not have a visible peak to determine the skewness. It is platy kurtosis as there is not peak.
Chapter 10 Solutions
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