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StatisticsEssentials Of StatisticsCompute the standard deviation for both sets of data presented in problem 3.13 and reproduced here. Compare the standard deviation computed for freshmen with the standard deviation computed for seniors. What happened? Why? Does this change relate to what happened to the mean over the four-year period? How? What happened to the shapes of the underlying distribution? Freshmen 10 43 30 30 45 40 12 40 42 35 45 25 10 33 50 42 32 38 11 47 22 26 37 38 10 Seniors 10 45 35 27 50 35 10 50 40 30 40 10 10 37 10 40 15 30 20 43 23 25 30 40 10 3.13 S O C A sample of 25 freshmen at a major university completed a survey that measured their degree of racial prejudice (the higher the score, the greater the prejudice). a. Compute the median and mean scores for these data. 10 43 30 30 45 40 12 40 42 35 45 25 10 33 50 42 32 38 11 47 22 26 37 38 10 b. These same 25 students completed the same survey during the senior year. Compute the median and mean for this second set of scores, and compare them to the earlier set. What happened? 10 45 35 27 50 35 10 50 40 30 40 10 10 37 10 40 15 30 20 43 23 25 30 40 10BuyFind*arrow_forward*

4th Edition

HEALEY + 1 other

Publisher: Cengage Learning,

ISBN: 9781305093836

Chapter 4, Problem 4.17P

Textbook Problem

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Compute the standard deviation for both sets of data presented in problem 3.13 and reproduced here. Compare the standard deviation computed for freshmen with the standard deviation computed for seniors. What happened? Why? Does this change relate to what happened to the mean over the four-year period? How? What happened to the shapes of the underlying distribution?

Freshmen |
||||

10 | 43 | 30 | 30 | 45 |

40 | 12 | 40 | 42 | 35 |

45 | 25 | 10 | 33 | 50 |

42 | 32 | 38 | 11 | 47 |

22 | 26 | 37 | 38 | 10 |

Seniors |
||||

10 | 45 | 35 | 27 | 50 |

35 | 10 | 50 | 40 | 30 |

40 | 10 | 10 | 37 | 10 |

40 | 15 | 30 | 20 | 43 |

23 | 25 | 30 | 40 | 10 |

**3.13**

**a.** Compute the median and mean scores for these data.

10 | 43 | 30 | 30 | 45 |

40 | 12 | 40 | 42 | 35 |

45 | 25 | 10 | 33 | 50 |

42 | 32 | 38 | 11 | 47 |

22 | 26 | 37 | 38 | 10 |

**b.** These same 25 students completed the same survey during the senior year. Compute the median and mean for this second set of scores, and compare them to the earlier set. What happened?

10 | 45 | 35 | 27 | 50 |

35 | 10 | 50 | 40 | 30 |

40 | 10 | 10 | 37 | 10 |

40 | 15 | 30 | 20 | 43 |

23 | 25 | 30 | 40 | 10 |

Expert Solution

To determine

**To find:**

The standard deviation for freshmen and seniors and compare them.

**Given:**

The following table shows the scores of 25 freshmen.

10 | 43 | 30 | 30 | 45 |

40 | 12 | 40 | 42 | 35 |

45 | 25 | 10 | 33 | 50 |

42 | 32 | 38 | 11 | 47 |

22 | 26 | 37 | 38 | 10 |

The following table shows the scores of 25 seniors.

10 | 45 | 35 | 27 | 50 |

35 | 10 | 50 | 40 | 30 |

40 | 10 | 10 | 37 | 10 |

40 | 15 | 30 | 20 | 43 |

23 | 25 | 30 | 40 | 10 |

**Formula used:**

Let the data values be

The formula to calculate mean is given by,

The formula to calculate standard deviation is given by,

Where,

**Calculation:**

For the freshmen,

The size of the population is 25.

The mean is given by,

Substitute 25 for

Consider the following table of sum of squares,

10 | 471.7584 | |

40 | 8.28 | 68.5584 |

45 | 13.28 | 176.3584 |

42 | 10.28 | 105.6784 |

22 | 94.4784 | |

43 | 11.28 | 127.2384 |

12 | 388.8784 | |

25 | 45.1584 | |

32 | 0.28 | 0.0784 |

26 | 32.7184 | |

30 | 2.9584 | |

40 | 8.28 | 68.5584 |

10 | 471.7584 | |

38 | 6.28 | 39.4384 |

37 | 5.28 | 27.8784 |

30 | 2.9584 | |

42 | 10.28 | 105.6784 |

33 | 1.28 | 1.6384 |

11 | 429.3184 | |

38 | 6.28 | 39.4384 |

45 | 13.28 | 176.3584 |

35 | 3.28 | 10.7584 |

50 | 18.28 | 334.1584 |

47 | 15.28 | 233.4784 |

10 | 471.7584 | |

From equation

Square the both sides of the equation.

Proceed in the same manner to calculate

The standard deviation is given by,

From equation

Essentials Of Statistics

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