Chapter 5, Problem 26P

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10th Edition

Frederick J Gravetter + 1 other

ISBN: 9781305504912

Textbook Problem

A sample consists of the following

a. Compute the mean and standard deviation for the sample.

b. Find the *z*-score for each score in the sample.

c. Transform the original sample into a new sample with a mean of

To determine

- Mean and standard deviation for the sample.
- Z-score for each score in the sample.
- Transform the original sample into a new sample with a mean of M = 50 and s = 10.

Explanation

**Given:**

n = 7

Scores: 5,0,4,5,1,2,4

M = 50

s = 10

**Formula used:**

**Calculation:**

- Sample mean = (5+0+4+5+1+2+4)/7 = 3
- z-scores are:

X | (x-xbar)2 |

5 | 4 |

0 | 9 |

4 | 1 |

5 | 4 |

1 | 4 |

2 | 1 |

4 | 1 |

21 | 24 |

Sample standard deviation =

5,0,4,5,1,2,4

For x = 5,

Z = (5 − 3) / 2 = 1

For x = 0,

Z = (0-3) / 2 = -1.5

In this way we will find all the z-scores.

X | z-scores |

5 | 1 |

0 | -1 |

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