The infant mortality rate is deﬁned as the number of infant deaths per 1,000 live births. This rate is often used as an indicato

Question

3 months ago

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The infant mortality rate is deﬁned as the number of infant deaths per 1,000 live births. This rate is often used as an indicato

r of the level of health in a country. The relative frequency histogram below shows the distribution of estimated infant death rates for 224 countries for which such data were available in 2014.31
(a) Estimate Q1, the median, and Q3 from the histogram.
(b) Would you expect the mean of this data set to be smaller or larger than the median? Explain your reasoning.
The graph that goes with it is in the picture.

Mathematics

1 answer:

tester [12.3K] · Answer 1 · 2026-02-24T04:01:25+03:00

(a)

Q1, or the first quartile, is at least 1/4 of the data points. It falls within the first bar, leading to an estimation of Q1=5. However, since this bar contains values ranging from 0 to around 9 or 10 (exactly unclear), and comprises almost 37% of the points, we might estimate Q1 slightly higher, around Q1=7.

The median must exceed half the points. With the first bar at 37% and the next at 22%, it is positioned roughly halfway in the second bar, giving median=15.

The third bar holds 11%, totaling 70% so far. The fourth bar includes 5%, placing us toward the end of the fourth bar for Q3, the third quartile, or 75th percentile, approximately Q3=40.

b

When data is significantly skewed to the left, as seen here, the median is typically lower than the mean. The 5% of data ranging from 80 to 120 averages around 100, contributing 5 to the mean, while 8% from 60 to 80 adds an additional 5.6, and 15% from 40 to 60 adds roughly 7.5. Consequently, the mean will likely be much higher than the median, which is around 15.