Help with this maths questions!

[Tweek]

This seemingly elementary stats question stumped me. Anyone can help?

IN a test for eyesight, for which the scores vary from 0 to 6, the table below shows the distribution of these scores for some volunteers who took part in the test.

Score of < 2: 10 volunteers
Score of 2: 7 volunteers
Score of 3: 8 volunteers
Score of 4: x volunteers
Score of >= 5: 8 volunteers

If the mean score is 3, find the value of x.

The correct answer is 12.

maths whiz, fire away!

 

[canonsiao]

This seemingly elementary stats question stumped me. Anyone can help?

IN a test for eyesight, for which the scores vary from 0 to 6, the table below shows the distribution of these scores for some volunteers who took part in the test.

Score of < 2: 10 volunteers
Score of 2: 7 volunteers
Score of 3: 8 volunteers
Score of 4: x volunteers
Score of >= 5: 8 volunteers

If the mean score is 3, find the value of x.

The correct answer is 12.

maths whiz, fire away!

For score <2, use the midpoint of 0 and 1: 0.5
For score >=5, use the midpoint of 5 and 6: 5.5

Then use the formula Summation f(x) / Sum of x = 3

To help you further:

[0.5(10) + 2(7) + 3(8) + 4x + 5.5(8)] / (33+x) = 3

 

[Tweek]

For score <2, use the midpoint of 0 and 1: 0.5
For score >=5, use the midpoint of 5 and 6: 5.5

Then use the formula Summation f(x) / Sum of x = 3

that's right! I never did much of stats in my whole life of education, is this assumption of using the midpoint a standard practice?

 

[Siddhi]

that's right! I never did much of stats in my whole life of education, is this assumption of using the midpoint a standard practice?

That depends. Since no information of the distribution between 0 & 1 is given, you can generally assume that the 10 people are uniformly distributed between the two. Similarly for between 5 & 6. Sometimes more information about the distribution is known, so in those cases you cannot assume like this.