# Statistics problems Test Problems

**URL:** <https://talk.achievable.me/t/statistics-problems-test-problems/793>\
**Category:** Quantitative reasoning\
**Created:** [September 23, 2021, 1:30am UTC](https://talk.achievable.me/t/statistics-problems-test-problems/793 "2021-09-23T01:30:06Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![Ana2](https://talk.achievable.me/letter_avatar/ana2/32/6_22734026db12803ebb3e059622ac3534.png) [@Ana2](https://talk.achievable.me/u/Ana2)\
**Post date:** [September 23, 2021, 1:30am UTC](https://talk.achievable.me/t/statistics-problems-test-problems/793/1 "2021-09-23T01:30:06Z")

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Hi there,

I am going through the “Statistics problems” section and found that the answers to the below question made sense. However, when going to the review section, it seems like only the mean average matters as the median is discarded. Can anyone please provide clarity on why this is?

Test question:

> _The following table indicates the number of paying customers at a local restaurant by week._

|Week number|Number of customers|

|1|23|  
|2|67|  
|3|198|  
|4|13|  
|5|x|  
|6|100|

> For what values of _x_ are both the mean and the median of paying customers for the entire six-week period between 70 and 80?

> _Indicate all that apply._

> a. 70  
> b. 72  
> c. 74  
> d. 78  
> e. 81  
> f. 84

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<div class="post-metadata">

**Author:** ![Ana2](https://talk.achievable.me/letter_avatar/ana2/32/6_22734026db12803ebb3e059622ac3534.png) [@Ana2](https://talk.achievable.me/u/Ana2)\
**Post date:** [September 23, 2021, 1:59am UTC](https://talk.achievable.me/t/statistics-problems-test-problems/793/2 "2021-09-23T01:59:20Z")

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![image](https://d2a8kmyc1dvkyq.cloudfront.net/original/1X/f950279c5cdcf1cf01384a998119c8d4e20e162d.jpeg)

FYI: I am referring to the solution offered for CYY64-RBG6D

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<div class="post-metadata">

**Author:** ![Justin](https://talk.achievable.me/user_avatar/talk.achievable.me/justin/32/41_2.png) [@Justin](https://talk.achievable.me/u/Justin)\
**Post date:** [September 23, 2021, 6:54am UTC](https://talk.achievable.me/t/statistics-problems-test-problems/793/3 "2021-09-23T06:54:20Z")

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Hi @Ana2, welcome to Achievable!

The trick here is in the list of numbers, and which numbers get used in the median calculation:

Textbook version: 13, 23, **67** , 100, 198 (median: **67** )  
Quiz version: 50, 65, **65** , 71, 90 (median: **65** )

Let’s think about what would happen if we added in the number 31.

Textbook version: 13, 23, _ **31** _, **67** , 100, 198 (median changed: **49** )  
Quiz version: _31_, 50, **65** , **65** , 71, 90 (median unchanged: **65** )

So basically, for the quiz version, any number that is \<=65 or \>=71 will not change the median. Since the current list’s median falls within the range already, we can essentially ignore that condition.