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? What is the median?
(b) Comment on the data's modality (i.e., bimodal, trimodal, etc.).
(c) Can you find (roughly) the first quartile (Q1) and the third quartile (Q3) of the data?
(e) Give the five-number summary of the data.
(f) Show a boxplot of the data.
(g) How is a quantile-quantile plot different from a quantile plot?
Answers
Answer:
a) What is the mean of the data? What is the median?
Ans : Mean = Sum of all values / No. of values
= 809 / 27
= 29.96
Median (since no. of total data values are odd) = (n+1)/2 th value
= (27+1)/2 th value
= 14 th value
= 25
b) Comment on Data’s modality
Ans: 13,15,19,21,30,36,40,45,46,52,70 occurs once in the data set.
16,20,22,33 occurs twice in the data set.
25,35 occurs four times in the data set.
Hence, this data set is bimodal with two modes as 25 and 35.
c) Can you find the first quartile and third quartile of the data?
Ans : First Quartile (Q1 ) = 25 th Percentile of the data
= (25*27)/100
= 6.75 = 7 th value
= 20
Third Quartile (Q3 ) = 75 th Percentile of the data
= 20 th value
= 35
d) Give the five number summary of the data?
Ans: Five number summary :
Minimum = 13, Q1 = 20, Median = 25, Q3 = 35, Maximum = 70
f ) How is Quantile-Quantile plot different from Quantile plot?
Ans : Quantile plot is a simple and effective way to have a first look at a univariate data distribution , while Quantile-Quantile plot graphs the quantiles of one univariate distribution against the corresponding quantiles of another. Hence, Q-Q plot is a powerful visualisation tool in that it allows the user to view whether there is a shift in going from one distribution to another .
Explanation: