The Editor’s Report in the November 2003 issue of lechnometrics provides the following information regarding the length of time taken to review articles that were submitted for publication during the year 2002. A few articles took longer than 9 months to review, these are omitted from the table.

Time (months) |
Number of Articles |

0-<1 |
45 |

l-< 2 |
17 |

2-< 3 |
18 |

3-< 4 |
19 |

4-< 5 |
12 |

5-< 6 |
14 |

6-< 7 |
13 |

7-< 8 |
22 |

8-< 9 |
11 |

a. Construct a histogram for these data.

b. Which class interval contains the median review time?

c. Which class interval contains the first quartile of the review times?

d. Which class interval contains the third quartile of the review times?

Answer :

Step 1 of 4 :

The editor’s Report on the November 2003 the article that was submitted for publication during the year 2002.

A few articles took longer than 9 months to review.

Then the data is given below.

Time (months) |
Number of Articles |

0-<1 |
45 |

l-< 2 |
17 |

2-<3 |
18 |

3-<4 |
19 |

4-<5 |
12 |

5-<6 |
14 |

6-<7 |
13 |

7-<8 |
22 |

8-<9 |
11 |

Our goal is to find

a). Construct a histogram of these data.

b). Which class interval contains the median review time.

c). Which class interval of the first quartile of the review time.

d). Which class interval of the third quartile of the review time.

a).

Now we have to construct a histogram of these data.

Then the histogram is given below.

Step 2 of 4 :

b).

Now we have to find the which class interval contains the median review time.

Consider the data

Time (months) |
Number of Articles |

0-<1 |
45 |

l-< 2 |
17 |

2-<3 |
18 |

3-<4 |
19 |

4-<5 |
12 |

5-<6 |
14 |

6-<7 |
13 |

7-<8 |
22 |

8-<9 |
11 |

Total |
171 |

From the above table sample size is 171.

So the value of the position of the median is

86

From the given data we arranged in order.

In the data the middle most value is 17.

Hence the median is 17.

Then there are 45+17+18 = 80 values less than or equal to 3 (from the table), and

80+19 = 99 values less than or equal to 4.

Therefore 3-<4 class interval contains the median.