Kim G. answered • 01/23/21

Yale student pursuing MA in statistics and PhD in public health

Hi Umi! Good question - thankfully, all we need is a frequency table to come up with an estimate.

Since we don't know anything about the exact *number *of hours each person studied (except the range given in this table), I'd start by calculating the midpoint of each range. In particular, what's the value that's *exactly between* the endpoints of each category? Remember, we calculate the halfway point between two numbers by adding them together and dividing them by two:

HOURS | MIDPOINT | N |

0-3 | (3+0)/2 = 1.5 | 18 |

4-7 | (7+4)/2 = 5.5 | 16 |

8-11 | (11+8)/2 = 9.5 | 14 |

12-15 | (15+12)/2 = 13.5 | 10 |

16-19 | (19+16)/2 = 17.5 | 2 |

Now note that the column "N" denotes the number of times we see an observation that corresponds to a certain category. That means that we see eighteen observations between 0 and 3 hours, sixteen observations between 4-7 hours, fourteen observations between 8 and 11 hours, ten observations between 12 and 15 hours, and two observations between 16 and 19 hours.

Now, all we need to do is multiply each "MIDPOINT" and "N" value within a given row, and then take the sum:

MIDPOINT | N | MIDPOINT x N |

1.5 (0-3 hours) | 18 | 1.5 x 18 = 27 |

5.5 (4-7 hours) | 16 | 5.5 x 16 =88 |

9.5 (8-11 hours) | 14 | 9.5 x 14 = 133 |

13.5 (12-15 hours) | 10 | 13.5 x 10 = 135 |

17.5 (16-19 hours) | 2 | 17.5 x 2 = 35 |

Now, let's add the last column together: 27 + 88 + 133 + 135 + 35 = 418.

We've now estimated the *total number of hours* that the students have spent studying all together. Now, to get the average, we simply divide by the total number of students in the class. In this problem, we get that number by simply adding the N column together: 18+16+14+10+2 = 60.

Our final answer, therefore, is **418/60 = about 7.**

Hope this helps!

Stanton D.

And by the way, let's hope this incident taught the students involved something about keeping records carefully and in a permanent fashion, with back-up of the data. If they didn't learn that, they will "probably" soon become "statistics" in the business world, if you catch my drift .... -- Cheers, --Mr. d.01/23/21