Question

20. The article "Determination of Most Representative Subdivísion" J. of Energy Engr., 1993: 43-55) gave data on various characteristics of subdivisions that could be used in deciding whether to provide electrical power using overhead lines or underground lines. Here are the values of the variable x total length of streets within a subdivision: 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 thou- sands digit as the stem and the hundreds digit as the leaf, and comment on the various features of the display b. Construct a histogram using class boundaries 0, 1000, 2000, 3000, 4000, 5000, and 6000. What proportion

Answer 1

a. Construct a stem-and-leaf display using the thousands digit as the stem and the hundreds digit as the leaf, and comment on the various features of the display.

Answer:

Stem Le 0 12 33 34555599 1 0 0122 2346 8 8 2 1 1 1 2 3 4 4477 3 0 1 1 3 33 8 4 5 2 3 778 4 3 7

Various features of the display are:

The display has positive skewness.

A typical data value is somewhere in the low 2000's.

(b) Construct a histogram using class boundaries 0, 1000, 2000, 3000, 4000, 5000, and 6000. What proportion of subdivisions have total length less than 2000? Between 2000 and 4000? How would you describe the shape of the histogram?

Answer:

14 12 10 12 10 4 CD 1000 2000 3000 4000 5000 6000 Total lengtlh

What proportion of subdivisions have total length less than 2000?

Answer: The proportion of subdivisions that have a total length less than 2000 is:

$\boldsymbol{\frac{12+11}{47}=\frac{23}{47}=0.489}$

Between 2000 and 4000?

Answer: The proportion of subdivisions that have a total length between 2000 and 4000 is:

$\boldsymbol{\frac{10+7}{47}=\frac{17}{47}=0.362}$

How would you describe the shape of the histogram?

Answer: The display has positive skewness.