Subtle error in numeracy test question?

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Discussion Overview

The discussion revolves around a numeracy test question that involves calculating the number of employees based on average costs. Participants explore the implications of using average values and the assumptions necessary to derive conclusions from the given data.

Discussion Character

  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants argue that the average cost per employee per year does not provide sufficient information to determine the number of employees in the first quarter, as the cost could vary.
  • Others suggest that if the average cost per employee per year is known, it can be divided by four to find the average cost per employee per quarter.
  • A counterexample is presented to illustrate that the average costs can depend on the number of employees in different quarters, indicating that multiple variables are at play.
  • Some participants emphasize the need for assumptions to be stated when answering such test questions, while others argue that the questions typically do not require assumptions and may include a "cannot say" option.
  • There is a contention regarding the understanding of averages, with some asserting that the average for the first quarter cannot simply be assumed to be one-fourth of the annual average.

Areas of Agreement / Disagreement

Participants express differing views on the validity of using average costs to determine employee numbers, with no consensus reached on the assumptions required for the test question.

Contextual Notes

Participants highlight the limitations of the information provided in the question, including the potential variability in employee costs across different quarters and the implications of averaging.

Outlined
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They say the answer is 41412 / (1392 / 4) = 119.
I think you cannot say as they gave the average cost per employee per year so you know nothing about the cost per employee per year in the 1st Q so you cannot decide how many employees you got that quarter.
 
Last edited:
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Hi Outlined! :wink:
Outlined said:
They say the answer is 41412 / (1392 / 4) = 119.
I think you cannot say as they gave the average cost per employee per year so you know nothing about the cost per employee per year in the 1st Q so you cannot decide how many employees you got that quarter.

But if you know the average cost per employee per year is 1392,

then the average cost per employee per quarter must be 1392/4. :smile:

What is worrying you about that? :confused:​
 
tiny-tim said:
Hi Outlined! :wink:


But if you know the average cost per employee per year is 1392,

then the average cost per employee per quarter must be 1392/4. :smile:

What is worrying you about that? :confused:​

thanks for your reply, however the employees who work in Q1 are not necessarily the same as the one who work in Q2, Q3 or Q4. So you have to be cautious drawing conclusion from that.
 
it's an average! :smile:

what do you think averages are for?? :rolleyes:
 
let me give you a counterexample.

p1 is the number of people who work in Q1
pr is the number of people who work in Q2, Q3 and Q4.

Than the average costs per employee per year equals

1/4 * 1/p1 * 41412 + 3/4 *1/ pr * (167040 - 41412) = 1392

Two free variables so c1 can be everything!
 
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I see what you mean Outlined. The cost per employee could have been different in Q1. But since it's a test question you have to make enough assumptions to be able to give an answer. If you were awesome you'd state those assumptions, like "I assume the average cost per employee per year is the same as if the average is taken only over 1st quarter." Well there's probably a nicer way to put it :P
 
thanks for your reply, however with most of this kind of quesitons you do not have to make assumptions. In fact, some of this kind of exercises have the option (it is always multiple choice) "cannot say".
 
tiny-tim said:
it's an average! :smile:

what do you think averages are for?? :rolleyes:
But anyone who thinks the average for the first 1/4 of a year must be equal to 1/4 the average for the year does not understand averages!
 

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