- Construct a cumulative frequency distribution of the 20 brain volumes(cm3) listed below.

Use the classes 900-999, 1000-1099, and so on. (6-classes)

1005 963 1035 1027 1281 1272 1051 1079 1034 1070 1173 1079 1067 1104 1347 1439 1029 1100 1204 1160.Also find relative frequency for each class interval?

Solution:

Class | Frequency |

900-999 | 1 |

1000-1099 | 10 |

1100-1199 | 4 |

1200-1299 | 3 |

1300-1399 | 1 |

1400-1499 | 1 |

- Use data above in question 1 to build the frequency polygon. Is the distribution symmetric?

Solution:

The data is not symmetrical, it is skewed.

- Find the mean, mode, median, variance, Standard Deviation, and range of the following data:

1 | 4 | 2 |

2 | 5 | 1 |

3 | 6 | 3 |

4 | 7 | 4 |

5 | 8 | 1 |

Solution:

Mean | 3.733333 |

Mode | 1 and 4 |

Median | 4 |

Variance | 4.780952 |

Standard Deviation | 2.186539 |

Range | 7 |

- Find the mean and the Variance of the following sample data:

x | Frequency (f) |

1 | 5 |

2 | 6 |

4 | 9 |

8 | 6 |

12 | 4 |

Solution:

We work out the data as in the table below;

Average=∑fx∑f

=149/30

=4.97

Variance= (f(x-xbar)^2)/n

=398.6/30

=13.10

- Two dice with six faces are rolled, find the sample space and number of elements in the sample space. Also calculate the probability that the sum of the two faces is equal 6.

Solution:

The sample space is as;

The number of elements in the sample space is 36

For the sum, the outcome is as shown below;

The probability that the sum of the two faces is 6 is 5/36

- Use the Prison and Plea data in following table to calculate part a and b :

Guilty Plea | Plea of not Guilty | |

Sentenced to Prison | 392 | 58 |

Not Sentenced to Prison | 564 | 14 |

- If someone from the 1028 subjects is randomly selected, find the probability of selecting someone sentenced to prison.
- If someone from the 1028 subjects is randomly selected, find the probability of selecting someone sentenced to prison and entered a Guilty Plea.

Solution

- 450/1028

=0.4377

- 392/1028

=0.3813