Problem 18E

In a study of author productivity (“Lotka’s Test,” Collection Mgmt., 1982: 111–118), a large number of authors were classified according to the number of articles they had published during a certain period. The results were presented in the accompanying frequency distribution:

a. Construct a histogram corresponding to this frequency distribution. What is the most interesting feature of the shape of the distribution?

b. What proportion of these authors published at least five papers? At least ten papers? More than ten papers?

c. Suppose the five 15s, three 16s, and three 17s had been lumped into a single category displayed as “ ≥ 15.” Would you be able to draw a histogram? Explain.

d. Suppose that instead of the values 15, 16, and 17 being listed separately, they had been combined into a 15–17 category with frequency 11. Would you be able to draw a histogram? Explain.

Answer

Step 1 of 4

(a)

The number of articles published in a certain period is presented in the accompanying frequency distribution.

Number of papers |
Frequency |

1 |
784 |

2 |
204 |

3 |
127 |

4 |
50 |

5 |
33 |

6 |
28 |

7 |
19 |

8 |
19 |

9 |
6 |

10 |
7 |

11 |
6 |

12 |
7 |

13 |
4 |

14 |
4 |

15 |
5 |

16 |
3 |

17 |
3 |

We are asked to construct a histogram corresponding to this frequency distribution. What is the most interesting feature of the shape of the distribution?

Step to create the Histogram in Minitab:

- On the opening of Minitab, you will get session handler and worksheet like Excel worksheet.
- Enter the data into the worksheet (in this case Number of papers and Frequency).
- After entering the data go to a menu called Graph in menu panel.
- In the Graph menu select option Histogram, you will get one window of Histogram.
- Under the Histogram window, and select the simple graph option.
- After doing this, you will get another which will contain all the variables you have entered in the worksheet.
- Select the Number of papers variable as Graph variables.
- Click on Data Options… and select frequency tab, under that double click the Frequency variable into the Frequency variables option.
- After everything entered correctly, press ok and you will get the Histogram of your data.
- Right click on the graph you have just created and select the copy graph option.

Figure 1: Histogram of the data

The most interesting feature of the shape of the distribution is the heavy positive skewness of the data.