Question

In Massachusetts, eight individuals experienced an unexplained episode of vitamin D intoxication that required hospitalization; it was thought that these unusual occurrences might be the result of excessive supplementation of dairy milk. Blood levels of calcium and albumin--a type of protein--for each subject at the time of hospital admission are provided below. Calcium (mmol/l) Albumin (g/l) 2.92 43 3.84 42 2.37 42 2.99 40 2.67 42 3.17 38 3.74 34 3.44 42

a. Find the mean, median, standard deviation and range of the recorded calcium levels.
b. Compute the mean, median, standard deviation and range of the given albumin levels.
c. For healthy individuals, the normal range of calcium values is 2.12 to 2.74 mmol/l, while the range of albumin levels is 32 to 55 g/l. Do you believe that patients suffering from vitamin D intoxication have normal blood levels of calcium and albumin?

Answer 1

a i). mean = 3.142

a ii). median = 3.08

a iii). standard deviation = 0.5106788

b i) mean = 40.375

b ii) median = 42

b iii). standard deviation = 3.020761

c) No.

Explanation:

The first step is to extract the data for each observation:

Calcium (mmol/l) => 2.92, 3.84, 2.37, 2.99, 2.67, 3.17, 3.74, 3.44

Albumin (g/l) => 43, 42,42,40, 42, 38, 34, 42

We simply compute the statistics asked on the data for each cases. I adopted R programming, please see the code below. Meanwhile, the formula remain the same as you can find in most statistics textbooks.

#.... R code

ca = c(2.92, 3.84, 2.37, 2.99, 2.67, 3.17, 3.74, 3.44) #... Calcium (mmol/l)

al = c(43, 42,42,40, 42, 38, 34, 42) #... Albumin (g/l)

#... Calcium (mmol/l)

mean(ca)

median(ca)

sd(ca)

#... Albumin (g/l)

mean(al)

median(al)

sd(al)

#... if you run this on your R software, you obtain the values presented above.

c) We are told that the normal range of calcium values is 2.12 to 2.74 mmol/l, while the range of albumin levels is 32 to 55 g/l.

The mean of Calcium (mmol/l) = 3.142

The mean of Albumin (g/l) = 40.375

As observed, the mean values for the Calcium is not within the range of normal values of 2.12 to 2.74 mmol/l. However, the mean values for the Albumin is within the range of normal values of 32 to 55 g/l.

Therefore, I don't believe that patients suffering from vitamin D intoxication have normal blood levels of calcium but rather have normal blood level of Albumin.

That is, they have normal blood level of Albumin but abnormal blood level of Calcium. Therefore, since the two condition is not met, we conclude that the patients suffering from vitamin D intoxication does not have normal blood levels of calcium and albumin.