Question

Given Data:

(1)= low lead level (2)= medium lead level, (3)= high lead level

IQ: 85 (1), 94 (1), 97 (1), 86 (1), 86 (1), 107 (1), 91 (1), 99 (1), 115 (1), 50 (1), 93 (1), 98 (1), 100 (1), 94 (1), 73 (1), 76 (1), 72 (1), 76 (1), 95 (1), 89 (1), 96 (1), 108 (1), 74 (1), 72 (2), 90 (2), 100 (2), 91 (2), 98 (2), 91 (2), 85 (2), 97 (2), 91 (2), 78 (2), 82 (3), 93 (3), 89 (3), 94 (3), 88 (3), 83 (3), 76 (3).

N=40 Mean=88.8 Standard deviation= 11.92

3a) Find the 5-number summaries for IQ Full for population of medium lead levels and for the population of high lead levels.

b) Construct box and whisker plots using your 5-number summaries for both populations. Put them on the same scale. Compare and contrast the two populations using the box and whisker plots as your evidence.

Answer 1

a)

i)5-number summaries for IQ Full for population of medium lead level

Population size:10

Mean (μ): 89.3
Median: 91
Lowest value: 72
Highest value: 100
First quartile: 83.25
Third quartile: 97.25

Interquartile range: 14

ii)5-number summaries for IQ Full for population of high lead levels.

Population size: 7
Median: 88
Minimum: 76
Maximum: 94
First quartile: 82
Third quartile: 93
Interquartile Range: 11

b)

i)Box plot for IQ Full for population of medium lead level

ii) Box plot for IQ Full for population of high lead level

ii) box plot for using two population IQ Full for population of median lead level and high lead level

5-number summaries for median lead level and high lead level

Population size: 17
Median: 90
Minimum: 72
Maximum: 100
First quartile: 82.5
Third quartile: 93.5
Interquartile Range: 11