Math

StatisticsEssentials Of StatisticsS O C Labor force participation rates (percent employed), percent high school graduates, and mean income for males and females in ten states are reported here. Calculate the mean and the standard for both groups for each variable and describe the differences. Are males and females unequal on any of these variables? How great is the gender inequality? Labor Force Participation Rate Percentage HS Graduates Mean Income State Male Female Male Female Male Female A 65.8 54.3 81.0 81.9 55,623 50,012 B 76.7 63.0 88.4 89.7 52,345 51,556 C 71.8 57.2 82.4 84.6 55,789 48,231 D 76.1 66.6 89.5 90.9 48,907 46,289 E 75.1 63.1 86.9 88.7 62,023 58,034 F 69.9 61.1 86.3 86.4 55,000 53,897 G 73.6 59.6 87.1 87.6 49,145 47,148 H 70.5 60.3 87.0 87.6 51,897 50,659 I 66.3 55.2 81.7 84.1 51,238 45,289 J 74.5 67.1 89.1 91.6 60,746 56,489BuyFind*arrow_forward*

4th Edition

HEALEY + 1 other

Publisher: Cengage Learning,

ISBN: 9781305093836

Chapter 4, Problem 4.7P

Textbook Problem

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Labor Force Participation Rate |
Percentage HS Graduates |
Mean Income |
||||

State |
Male |
Female |
Male |
Female |
Male |
Female |

A | 65.8 | 54.3 | 81.0 | 81.9 | 55,623 | 50,012 |

B | 76.7 | 63.0 | 88.4 | 89.7 | 52,345 | 51,556 |

C | 71.8 | 57.2 | 82.4 | 84.6 | 55,789 | 48,231 |

D | 76.1 | 66.6 | 89.5 | 90.9 | 48,907 | 46,289 |

E | 75.1 | 63.1 | 86.9 | 88.7 | 62,023 | 58,034 |

F | 69.9 | 61.1 | 86.3 | 86.4 | 55,000 | 53,897 |

G | 73.6 | 59.6 | 87.1 | 87.6 | 49,145 | 47,148 |

H | 70.5 | 60.3 | 87.0 | 87.6 | 51,897 | 50,659 |

I | 66.3 | 55.2 | 81.7 | 84.1 | 51,238 | 45,289 |

J | 74.5 | 67.1 | 89.1 | 91.6 | 60,746 | 56,489 |

Expert Solution

To determine

**To find:**

The mean and standard deviation of male and female for the given variable

**Given:**

The following table shows the data of 3 different variables of 10 states.

Labor Force Participation Rate | Percentage HS Graduates | Mean Income | ||||

State | Male | Female | Male | Female | Male | Female |

A | 65.8 | 54.3 | 81.0 | 81.9 | 55, 623 | 50, 012 |

B | 76.7 | 63.0 | 88.4 | 89.7 | 52, 345 | 51, 556 |

C | 71.8 | 57.2 | 82.4 | 84.6 | 55, 789 | 48, 231 |

D | 76.1 | 66.6 | 89.5 | 90.9 | 48, 907 | 46, 289 |

E | 75.1 | 63.1 | 86.9 | 88.7 | 62, 023 | 58, 034 |

F | 69.9 | 61.1 | 86.3 | 86.4 | 55, 000 | 53, 897 |

G | 73.6 | 59.6 | 87.1 | 87.6 | 49, 145 | 47, 148 |

H | 70.5 | 60.3 | 87.0 | 87.6 | 51, 897 | 50, 659 |

I | 66.3 | 55.2 | 81.7 | 84.1 | 51, 238 | 45, 289 |

J | 74.5 | 67.1 | 89.1 | 91.6 | 60, 746 | 56, 489 |

**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:**

Consider the labor force participation rate for males.

The size of the population is 10.

The mean is given by,

Substitute 10 for

Consider the following table of sum of squares,

65.8 | 38.8129 | |

76.7 | 4.67 | 21.8089 |

71.8 | 0.0529 | |

76.1 | 4.07 | 16.5649 |

75.1 | 3.07 | 9.4249 |

69.9 | 4.5369 | |

73.6 | 1.57 | 2.4649 |

70.5 | 2.3409 | |

66.3 | 32.8329 | |

74.5 | 2.47 | 6.1009 |

From equation

Square the both sides of the equation.

Proceed in the same manner to calculate

The standard deviation is given by,

From equation

Thus, standard deviation for the labor force participation rate for males is 3.67.

Consider the labor force participation rate for females.

The mean is given by,

Substitute 10 for

Consider the following table of sum of squares,

54.3 | 41.6025 | |

63 | 2.25 | 5.0625 |

57.2 | 12.6025 | |

66.6 | 5.85 | 34.2225 |

63.1 | 2.35 | 5.5225 |

61.1 | 0.35 | 0.1225 |

59.6 | 1.3225 | |

60.3 | 0.2025 | |

55.2 | 30.8025 | |

67.1 | 6.35 | 40.3225 |

From equation

Square the both sides of the equation.

Proceed in the same manner to calculate

The standard deviation is given by,

From equation

Thus, standard deviation for the labor force participation rate for females is 4.144.

Consider the percentage HS graduates of males.

The mean is given by,

Substitute 10 for

Consider the following table of sum of squares,

81 | 24.4036 | |

88.4 | 2.46 | 6.0516 |

82.4 | 12.5316 | |

89.5 | 3.56 | 12.6736 |

86.9 | 0.96 | 0.9216 |

86.3 | 0.36 | 0.1296 |

87.1 | 1.16 | 1.3456 |

87 | 1.06 | 1.1236 |

81.7 | 17.9776 | |

89.1 | 3.16 | 9.9856 |

From equation

Square the both sides of the equation.

Proceed in the same manner to calculate

The standard deviation is given by,

From equation

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