Problem 29BSC

In Exercises, find the mean of the data summarized in the given frequency distribution. Also, compare the computed means to the actual means obtained by using the original list of data values, which areasfoüows: 35.9 years;

Age of Best Actress When Oscar Was Won |
Frequency |

20–29 |
27 |

30–39 |
34 |

40–49 |
13 |

50–59 |
2 |

60–69 |
4 |

70–79 |
1 |

80–89 |
1 |

Problem 29BSC

Answer:

Step1 of 3:

We have the data summarized in the given frequency distribution.

Age of Best Actress When Oscar Was Won |
Frequency |

20–29 |
27 |

30–39 |
34 |

40–49 |
13 |

50–59 |
2 |

60–69 |
4 |

70–79 |
1 |

80–89 |
1 |

SUM |
N=82 |

Step2 of 3:

We need to find the mean of the data summarized in the given frequency distribution. Also, compare the computed means to the actual means obtained by using the original list of data values, which areasfoüows: 35.9 years.

Step3 of 3:

consider,

Age of Best Actress When |
Frequency(f) |
x |
fx |

20–29 |
27 |
24.5 |
661.5 |

30–39 |
34 |
34.5 |
1173 |

40–49 |
13 |
44.5 |
578.5 |

50–59 |
2 |
54.5 |
109 |

60–69 |
4 |
64.5 |
258 |

70–79 |
1 |
74.5 |
74.5 |

80–89 |
1 |
84.5 |
84.5 |

N=82 |
2939 |

Where x is the mid value of class intervals and it is calculated by

and so on..

The mean of the data summarized in the given frequency distribution is given by

=

= 35.8414

35.8

This result is quite close to the mean of 35.9 years found by using the original list of data values.