1 The fivenumber summary for all student scores on an exam i

1. The five-number summary for all student scores on an exam is 40, 60, 70, 75, 79.

Suppose 100 students took the test.

How many STUDENTS had scores between 40 and 70?

2. Suppose we know that the mean heart disease death rate is 200 per 100K people and is normally distributed across 27 countries. Suppose we also know that the greatest death rate reported is 220 per 100K and the lowest death rate reported is 180 per 100K. What should be a statistically-savvy person\'s best guess as to the SD of this distribution?

Solution

The five-number summary represents the min, 25^thpercentile, median, 75^thpercentile, and max, respectively and in order. Since 40 is the min score and 70 is the median score, then 50% must have had scores between 40 and 70

Mean score = 64.8

stdev of the scores = 15.6

Total students who took the test = 100

five-number summary for all student scores on an exam is 40, 60, 70, 75, 79

40 to 70 represents 50% of the population

Hence no of students who got scores between 40 and 70 = 0.5 * 100 = 50

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2) Greatest death rate = 220 per 100k

Lowest death rate = 180 per 100k

Mean heart disease death rate is 200 per 100K

hence stdev = 20 (Difference between mean and lowest or greatest value)