Mock Test Q5, why the difference has to be 40-55 ? why cant it be any other value ?

[Tejasvi Hegde]

For Mock Test Q5

"The difference between the relative frequency of value 1 and the relative frequency of value 5 is 0.06. Find the median of the outcomes of rolling the die  "

Why it cant be 

x = 0.32 and z be 0.06 ?  both stand for difference of 0.06 ?

[Statistics 1 Support 1]

Hello Tejasvi,

Can you share the screenshot here so that I can have a look and let you know where you are going wrong? x and z are the frequencies of the outcomes of a die. So, how it can be 0.32 and 0.06?

Thanks

Nikita

Statistics course support team

[Tejasvi Hegde]

Hi Nikita,

Please find my explanation as below

[CG]

In this question we use the difference in relative frequency that is specified in the question to find x and z.

• x+y+z = 250 - 105 = 145
• x/250 - z/250 = 0.06 also z/250 - x/250 = 0.06 (wording of the question only specifies difference)
• y = 250 * 0.2 = 50
• Now we find x and z . It can be x = 55 and z = 40 or x=40 and z =55.
• The question that is asked will have the same answer which ever value of x and z you consider.
• Median = 250 *0.5 = 125th value

Writing the consolidated frequencies:

1 - 55 (or 40)

2 - 65 (or 50)

3 - 115 (or 100)

4 - 150 (or 135)      <- 125th value comes here in both cases.

5 - 190 (190)

6 - 250 (250)

This is sufficient to answer the question asked. 

Now if you find relative frequency of x and z, you get 0.16 and 0.22.

[Tejasvi Hegde]

But how is the calculation I showed is wrong ? isn't it not satisfying the requirement of difference of x and z be 0.06 ?

All totals are matching too.

Required difference of 0.06 between x and z will provide numerous combinations in reality.

[CG]

relative frequency of x - relative frequency of z = 0.06 [This is what the question says ]

In the image you have posted above :

•  relative frequency of x = 0.32
•  relative frequency of z = 0.06
•  0.32 - 0.06 = 0.26