Explanations 
Textbooks 
Flashcards 
91影视 AI 
Notes 
Study Plans 
Study Sets 
Find a degree 
Magazine Chapter 1: Q20E (page 25)
The article 鈥淒etermination of Most RepresentativeSubdivision鈥� (J. of Energy Engr., 1993: 43鈥�55) gavedata on various characteristics ofsubdivisions that couldbe used in deciding whether to provide electrical powerusing overhead lines or underground lines. Here are thevalues of the variable x=total length of streets within asubdivision:
1280 | 5320 | 4390 | 2100 | 1240 | 3060 | 4770 |
1050 | 360 | 3330 | 3380 | 340 | 1000 | 960 |
1320 | 530 | 3350 | 540 | 3870 | 1250 | 2400 |
960 | 1120 | 2120 | 450 | 2250 | 2320 | 2400 |
3150 | 5700 | 5220 | 500 | 1850 | 2460 | 5850 |
2700 | 2730 | 1670 | 100 | 5770 | 3150 | 1890 |
510 | 240 | 396 | 1419 | 2109 | ||
a. Construct a stem-and-leaf display using the thousandsdigit as the stem and the hundreds digit as theleaf, and comment on the various features of thedisplay.
b. Construct a histogram using class boundaries 0, 1000, 2000, 3000, 4000, 5000, and 6000. What proportion of subdivisions have a total length less than 2000? Between 2000 and 4000? How would you describe the shape of the histogram?
Short Answer
a.
The stem and leaf display is,
b.
The histogram is represented as,
Theproportion ofsubdivisions that have a total length less than 2000 is 0.489.
The proportion of subdivisions that have a total length between 2000 and 4000 is 0.489.
The shape of the histogram is right-skewed.
Step by step solution
Given information
Thedata on the total length of streets with a subdivisionis provided.
x represents the total length of streets within a subdivision.
Construct a stem and leaf display and state the features
a.
A stem-and-leaf display provides a visual representation of the dataset.
The steps to construct a stem-and-leaf display are as follows,
1) Select the leading digit for the stem and trailing digits for the leaves.
2) Represent the stem digits vertically and similarly the trailing digits corresponding to the stem digits.
3) Mention the units for the display.
The stem and leaf display for the provided scenario is,
The features that can be observed from the above display are,
1)The distribution is positively skewed.
2) There are no outliers present in the data.
Given information
Thedata on the total length of streets with a subdivision is provided.
x represents the total length of streets within a subdivision.
Construct a histogram and comment on the shape
b.
The size of the sample is 47.
The relative frequency is computed as,
\({\rm{relative frequency }} = \frac{{frequency}}{{Total\;number\;of\;observations}}\)
The table representing the relative frequency is computed as,
Class (x) | frequency | Relative frequency |
0-1000 | 12 | 0.255 |
1000-2000 | 11 | 0.234 |
2000-3000 | 10 | 0.213 |
3000-4000 | 7 | 0.149 |
4000-5000 | 2 | 0.043 |
5000-6000 | 5 | 0.106 |
Steps to construct a histogram are,
1) Determine the frequency or the relative frequency.
2) Mark the class boundaries on the horizontal axis.
3) Draw a rectangle on the horizontal axis corresponding to the frequency or relative frequency.
The histogram is represented as,
From the above-represented histogram, the shape of the distribution can be as positively skewed.
Compute the proportion
The proportion ofsubdivisions that have a total length less than 2000 is computed as,
\(\begin{aligned}P\left( {x < 2000} \right) &= 0.255 + 0.234\\ &= 0.489\end{aligned}\)
Therefore, the proportion of subdivisions that have a total length less than 2000 is 0.489.
Compute the proportion
The proportion ofsubdivisions that have a total length between 2000 and 4000 is computed as,
\(\begin{aligned}P\left( {2000 < x < 4000} \right) &= 0.213 + 0.149\\ &= 0.362\end{aligned}\)
Therefore, therequired proportion is 0.362
From the histogram, it can be observed that the distribution of the given data is skewed to the right.
Over 30 million students worldwide already upgrade their learning with 91影视!
