Chapter 3, Problem 3.10P

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ISBN: 9781305093836

Textbook Problem

*SOC**As the head of a social services agency, you believe that your staff of 20 social workers is very much overworked compared with 10 years ago. The case loads for each worker are reported below for each of the two years in question. Has the average caseload increased? Which measure of central tendency is most appropriate to answer this question? Why?*

2002 | 2012 | ||

52 | 55 | 42 | 82 |

50 | 49 | 75 | 50 |

57 | 50 | 69 | 52 |

49 | 52 | 65 | 50 |

45 | 59 | 58 | 55 |

65 | 60 | 64 | 65 |

60 | 65 | 69 | 60 |

55 | 68 | 60 | 60 |

42 | 60 | 50 | 60 |

50 | 42 | 60 | 60 |

To determine

**To find:**

The most appropriate measures of central tendency for each variable.

Explanation

**Description:**

When the variables measured have non-numerical scores or categories, they are said to have a nominal level of measurement.

When the variables measured have non-numerical scores or categories that could be ranked from high to low, they are said to have an ordinal level of measurement.

When the variables measured have numerical scores and can be used for further statistical analysis, they are said to have an interval ratio level of measurement.

From the given information, the variable **Caseload** has a numeric value; therefore, the level of measurement of this variable is interval-ratio.

**Choosing a Measures of Central Tendency:**

When the data is Nominal type — Mode

When the data is Ordinal type — Median

When the data is Interval ratio type — Mean

For the variable **Case load, the measure of central tendency is: Mean.**

**Formula Used:**

The formula to calculate mean is given by,

**For year 2002:**

Substitute 20 for

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