Find the means, medians, upper and lower values and interquartile ranges for each of the data sets:for girls: 9.72, 9.86, 10.29 , 10.59 , 11.02, 11.81, 12.37,12.75,12.89 ,13.01.   for...

Find the means, medians, upper and lower values and interquartile ranges for each of the data sets:

for girls: 9.72, 9.86, 10.29 , 10.59 , 11.02, 11.81, 12.37,12.75,12.89 ,13.01.

 

for boys: 

10.94 , 11.67 , 12.65 , 13.77, 14.04 , 14.82 , 15.49 , 16.44 , 17.16 , 18.53.


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giorgiana1976 | College Teacher | (Level 3) Valedictorian

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We'll find the requested means, medians, upper and lower values and interquartile ranges for girls set.

I'll use M and M method and I'll split the original set in half.

{9.72, 9.86, 10.29 , 10.59 , 11.02} {11.81, 12.37,12.75,12.89 ,13.01}

Since there are 5 terms in each half,the lower quartile is 10.29 and the upper quartile is 12.75.

Another method to determine the lower and upper quartiles is Sincich's Method.

We discover that we have 10 elements in the girls' set.

Lower quartile = L = (1/4)*(10+1) = 11/4 = 2.75

We'll round the result to the nearest integer, that is n = 3.

The lower quartile is the 3rd element from the set.

L = 10.29

Upper quartile:

U = (3/4)*(10+1)

U = 33/4 = 8.25

We'll round the result to the nearest integer, that is n = 8.

The upper quartile is the 8th element from the set.

U = 12.75

We'll do the same fot the boys' set that contains also 10 elements.

Lower quartile = L = (1/4)*(10+1) = 11/4 = 2.75

We'll round the result to the nearest integer, that is n = 3.

The lower quartile is the 3rd element from the set.

L = 12.65

Upper quartile:

U = (3/4)*(10+1)

U = 33/4 = 8.25

We'll round the result to the nearest integer, that is n = 8.

The upper quartile is the 8th element from the set.

U = 16.44

The requested lower and upper quartiles for girls' set are:L = 10.29 and U = 12.75 and lower and upper quartiles for boys' set are:L = 12.65 and U = 16.44.

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