Question

Five Number Summary for Percent Obese by State

Computer output giving descriptive statistics for the percent of the population that is obese for each of the US states, from the USStates dataset, is given in the table below.

Descriptive Statistics: Obese

Variable N    N^*    Mean          SE Mean     StDev       Minimum    Q1             Median Q3            Maximum

Obese         50   0         28.766        0.476          3.369       21.300        26.375       29.400      31.150      35.100

Percent of the population that is obese by state

(a) What is the five number summary?

The five number summary is :

(b) Give the range and the IQR.

The range is

The IQR is

(c) What can we conclude from the five number summary about the location of the 35 ^th percentile? The 70 ^th percentile?

The location of the 35^th percentile is between ----------------- and -----------------

The location of the 70 ^th percentile is between -------------------- and ----------------

Answer 1

Given:

Five Number Summary for Percent Obese by State Computer output giving descriptive statistics for the percent of the population that is obese for each of the US states, from the USStates dataset, is given in the table below.

Variable	N	N*	Mean	SE mean	StDev	Minimun	Q1	Median	Q3	Maximum
Obese	50	0	28.766	0.476	3.369	21.300	26.375	29.400	31.150	35.100

a) The five number summary is

Minimum = 21.300

First quartile, Q1 = 26.375

Median = 29.400

Third quartile, Q3 = 31.150

Maximum = 35.100

b) The range and the IQR:

The range = Maximum value - Minimum value

= 35.100-21.300 = 13.800

Inter quartile range, IQR = Q3-Q1

= 31.150-26.375

= 4.775

The range is 13.800

The IQR is 4.775

c) The location of the 35th percentile is between Q1 and Q2 (median).

So The location of the 35th percentile is between 26.375 and 29.400

The location of the 70 th percentile is between Q2( median) and Q3.

So The location of the 70 th percentile is between 29.400 and 31.150