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

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Basic Math

The risk of developing iron deficiency is especially high duringpregnancy. Consider the following data on transferrin receptorconcentration (mg/L) for a sample of women with laboratory evidenceof overt iron-deficiency anemia. Please answer each question belowshowing 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 forthese 11 women?

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

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

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

Answer & Explanation Solved by verified expert
4.3 Ratings (662 Votes)

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
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