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4th Edition

HEALEY + 1 other

Publisher: Cengage Learning,

ISBN: 9781305093836

Chapter 4, Problem 4.1P

To determine

**To find:**

The range and standard deviation of the given scores

Expert Solution

**Solution:**

The range and standard deviation of the given scores is 40 and 12.28 respectively.

The given scores are,

**Formula used:**

The formula to calculate the range is,

Let the data values be

The formula to calculate the mean is,

The formula to calculate the standard deviation is,

Where,

**Calculation:**

Arrange the given data in increasing order.

The data in increasing order is given by,

The highest score is 50 and the lowest score is 10.

The range is given by,

Substitute 50 for high score and 10 for low score in the above mentioned formula,

The range of population is 40.

The size of the population is 10.

The mean is given by,

Substitute 10 for

Consider the following table of sum of squares,

Scores |
||

10 | 285.61 | |

12 | 222.01 | |

15 | 141.61 | |

20 | 47.61 | |

25 | 3.61 | |

30 | 3.1 | 9.61 |

32 | 5.1 | 26.01 |

35 | 8.1 | 65.61 |

40 | 13.1 | 171.61 |

50 | 23.1 | 533.61 |

From equation

Square both sides of the equation.

Proceed in the same manner to calculate

The formula to calculate the standard deviation is given by,

From equation

Thus, range is 40 and standard deviation is 12.28.

**Conclusion:**

Therefore, the range and standard deviation of the given scores is 40 and 12.28 respectively.

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