2. (21) The five-number summary for the number of house boats on each lake in Mi

Question

2. (21) The five-number summary for the number of house boats on each lake in Minnesota is given: Min-12, First quartile-18, Median-23, Third quartile-26, Max-39. The five- number summary suggests that: About 75% of lakes in Minnesota have more than how many house boats? a. b. About what percent of lakes in Minnesota have between 23 and 26 house boats? c. About 50% of lakes in Minnesota have more than how many house boats? d. Find the range of the number of house boats. e. Find the lower and upper bounds to identify outliers.

Explanation / Answer

Soln,

Since Quartlie or 5 pint summary describes the distribution of data without knowing all the data it overall indicates about the distribution of data or any outliers if any.

Ler given data as ,

Min =12 tthat means minimum no of boats are in lakes ,Q1= 18, that means 1st 25 % of data contains 18 boats

Q2= 23 median that is 50 % of first data lies to the lefta nd right of the median.

Q3= 26 is the 75 % of lakes have less than 26 boats .

Max= 39 that means there is maximum no of 39 boats .

2. a). From The Quartiles value it is clear that 75 % of lakes have more than 18 house boats .

It can be found by looking at quartile 1 which shows taht 25 % of lakes have less tah 18 boat.

b) Fom the Quartiles value it is evident that from Q2 to Q3 values there lies 25 % of lakes , or can be said that 25 % of lakes lies between 23 to 26.

c) Again from the Quartile values if we look at Q2= median , the data lies is 50 % at that point .

Hence More than 23 boats are there in 50 % of lakes.

d) Range of data is defined ad the diierence between the maxim value to minimum value of the data set.

So Range = Maximum - Minimum

= 39 -12 = 27, hence 27 is the range of data set of house boats in lakes.

e) The lower and upper bounds can be defined sa the limts beyond which if any data set lies that will called as outliers.

for this first we have to find IQR( inter quartile range) rhat can be found by

Q3-Q1 = IQR

= 26-18= 8

hence 8 is the IQR

So, first IQR*1.5= 8*1.5= 12

The upper boundry limit is Q3+12 = 26+ 12= 38

and our maximum limit is 39 which is pass 38 so we can say that it is an outlier.

Again for lower boundry limit

Q1-12 = 18-12= 6,

Since Minimus in inside the lower boundry limit so here is only one outlier.

so, Lower bound= 6

     Upper bound = 38

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