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Explain the relative positioning of the bars in a histogram to the numbers that label the horizontal axis when each of the following quantities is used to label that axis.

a. Lower class limits

b. Lower class cut points

c. Class marks

d. Class midpoints

Short Answer

Expert verified

Parta: Lower class limits: In the histogram the bars should be touches each other. The relative positioning of the bars in a histogram which extends horizontally from the lower limit of the class to the lower limit of the next class.

Partb: Lower cut points: In the histogram the bars should be touches each other. The relative positioning of the bars in a histogram which extends horizontally from the lower cut point of the class to the lower cut point of the next class.

Partc: Class mark: In the histogram the bars should be touches each other. The relative positioning of the bars in a histogram is centered horizontally over the mark of the class.

Part d: Class midpoints: In the histogram the bars should be touches each other. The relative positioning of the bars in a histogram is centered horizontally over the midpoint of the class.

Step by step solution

01

Part a Step 1. Given information

We need to explain the relative positioning of the bars in a histogram to the numbers that label the horizontal axis when each of the following quantities is used to label that axis.

02

Part a Step 2.Lower class limits:  

In the histogram the bars should be touches each other. The relative positioning of the bars in a histogram which extends horizontally from the lower limit of the class to the lower limit of the next class.

For example, let us the histogram which representing the frequency distributions for the data on days to maturity for short-term investments.

From the diagram, let us consider30-39. Here, the lower class limit is,30.

03

Part b Step 1.Lower cut points: 

In the histogram the bars should be touches each other. The relative positioning of the bars in a histogram which extends horizontally from the lower cut point of the class to the lower cut point of the next class.

For example, let us consider the histogram which representing the frequency distribution for the data on weights of males.

From the diagram, let us consider120-under140. Here, the lower class cut point is,120.

04

Part c Step 1.Class mark:  

In the histogram the bars should be touches each other. The relative positioning of the bars in a histogram is centered horizontally over the mark of the class.

For example, let us consider the histogram which representing the frequency distributions for the data on days to maturity for short-term investments.

From the diagram, let us consider 30-39.Here, the class mark is,30+392=692=34.5.

05

Part d Step 1.Class midpoints: 

In the histogram the bars should be touches each other. The relative positioning of the bars in a histogram is centered horizontally over the midpoint of the class.

For example, let us consider the histogram which representing the frequency distribution for the data on weights of males.

From the diagram, let us consider120-under140.Here, the class midpoint is,120+1402=2602=130.

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Most popular questions from this chapter

Explain the meaning of

Qualitative Variable

Discrete, Quantitative Variable

Continuous, Quantitative Variable

For instance, consider the grouped days-to-maturity data given in Table 2.10(b) on page 57.

From that table, we see that the cumulative frequency of investments with a maturity period of less than 50day is 4(3+1)and, therefore, the cumulative relative frequency is0.1(4/40).

Table 2.14shows all cumulative information for the days-to-maturity data.

Cumulative information for days-to-maturity data.

a. Round each observation to the nearest year and then construct a stem-and-leaf diagram of the rounded data.

b. Truncate each observation by dropping the decimal part, and then construct a stem-and-leaf diagram of the truncated data.

c. Compare the stem-and-leaf diagrams that you obtained in parts (a) and (b).

We used slightly different methods for determining the "middle" of a class with limit grouping and cut point grouping. Identify the methods and the corresponding terminologies.

Clocking the Cheetah. Refer to the speed data given in Exercise 2.89.

a. Construct a table similar to Table 2.14for the data, based on the classes specified in Exercise 2.89. Interpret your results.

b. Construct an ogive for the data.

A variable of a population has a left-skewed distribution.

a. If a large simple random sample is taken from the population, roughly what shape will the distribution of the sample have? Explain your answer.

b. If two simple random samples are taken from the population, would you expect the two sample distributions to have identical shapes? Explain your answer.

c. If two simple random samples are taken from the population, would you expect the two sample distributions to have similar shapes? If so, what shape would that be? Explain your answers.

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