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The risk of developing iron deficiency is especially high during pregnancy. Consider the following data on...

The risk of developing iron deficiency is especially high during pregnancy. Consider the following data on transferrin receptor concentration (mg/L) for a sample of women with laboratory evidence of overt iron-deficiency anemia. Please answer each question below showing all calculations by hand.

11.2, 10.5, 7.6, 11.3, 10.4, 9.7, 20.8, 9.4, 19.5, 9.4, 8.3

(a) What is the median transferrin receptor concentration for these 11 women?

(b) What is the mean transferrin receptor concentration for these 11 women?

(c) Do you regard the mean or the median as more representative of the center of the data? Explain your choice.

(d) What are the variance and standard deviation for transferrin receptor concentrations of these 11 women?

Solutions

Expert Solution

a)

Median=0.5(n+1)th value =    6th   value of sorted data
=   10.400  

b)

mean =    ΣX/n =    128.100   /   11   =   11.6455
.

c)

mean > median , so data is skewed

so, median is more representative of the center of the data

d)

X (X - X̄)²
11.2 0.198
10.5 1.312
7.6 16.366
11.3 0.119
10.4 1.551
9.7 3.785
20.8 83.806
9.4 5.042
19.5 61.694
9.4 5.042
8.3 11.192
X (X - X̄)²
total sum 128.1 190.11
n 11 11

sample variance =    Σ(X - X̄)²/(n-1)=   190.1073   /   10   =   19.011
                      
sample std dev =   √ [ Σ(X - X̄)²/(n-1)] =   √   (190.1073/10)   =       4.3601

milcah answered 1 year ago
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