Exercise 8 - Data Central Tendency

Suppose that the data for analysis includes the attribute age. The age values for the data tuples are (in increasing order) 13, 15, 16, 16, 19, 20, 20, 21, 22, 22, 25, 25, 25, 25, 30, 33, 33, 35, 35, 35, 35, 36, 40, 45, 46, 52, 70.

(a) What is the mean of the data?

(b) What is the median?

(d) What is the midrange of the data?

(e) Can you find (roughly) the first quartile (Q1) and the third quartile (Q3) of the data?

(f) Give the five-number summary of the data.

Solution:

a) Total No of age values given = 27

Mean of the data = 809/27 = 29.96

The mean age value is 29.96

b) Median, center of the data is 14th value.

The median age value is 25

c) mode, the value that occurs most frequently in the set.

The data set is multimodal. The mode are 25 and 35.

d) Midrange, average of the smallest and largest value in the data set.

smallest value = 13

largest value = 70

midrange = 83/2 = 41.5

The midrange age value is 41.5

e) First quartile (Q1) & Third quartile (Q3)

Median (Q2) = 25

First Quartile (Q1) = 20

Third Quartile (Q3) = 35

The first quartile (Q1) age value is 20 and third quartile (Q3) age value is 35

f) Five number summary

Minimum, Q1, Median, Q3, Maximum.

The five number summary of age value is 13, 20, 25, 35, 70

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