Question

Suppose a lab has a mix of blood samples from a group of male patients and female patients.¹  The average number of red blood cells detected by the machine among the male blood samples was 5.8 million/mm³, the average number of red blood cells detected by the machine among the female blood samples was 4.2 million/mm³, and the average number of red blood cells detected by the machine among all blood samples was 5.4 million/mm³.

A. Does the lab have more female or male blood samples? How do we know this?

B. What is the ratio of male to female blood samples?

Answer 1

(A) The Lab has more Male samples. This is illustrated as below.

Let M be the number of males and F be the number of females

Total blood samples of males + Total Blood samples of females = Total of all blood samples.

Given, Average blood sample for males = 5.4, for females = 4.8 and for all = 5.4 million / mm³.

Average = Sum of observations / Total observations. Therefore Sum of observations = Average * Total Observations

5.8 M + 4.2 F = 5.4 (M + F)

5.8 M + 4.2F = 5.4M + 5.4F

0.4M = 1.2F

Therefore M = 3F. I.e if F = 1, then M = 3. Therefore there are more men than women.

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B) We have found in A, that M = 3F

Therefore M / F = 3 / 1

i.e The Ratio M : F = 3 : 1

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