Use the data set and the indicated number of classes to construct (a) an expanded frequency distribution, (b) a frequency histogram, (c) a frequency polygon, (d) a relative frequency histogram, and (e) an ogive.

hospitals
number of classes: 8
data set: number of hospitals in each state
12 100 52 73 354 52 34 8 212 116
13 40 17 142 99 61 76 114 81 50
22 109 56 88 72 16 103 11 28 14
75 37 28 203 156 103 36 176 12 65
27 116 377 35 89 7 62 75 39 13

a)                                                                                                       Cumulative

        Relative       cumulative  Relative

Class intervalmidpoint  frequencyfrequency   frequency  frequency

0 -50       25    20    0.40            20    0.40    

50 -100       75    16            0.32             36    0.72    

100 -150       125    8            0.16             44    0.88    

150 -200      175    2            0.4             46    0.92    

200 -250     225           2            0.4             48    0.96    

250 -300     275           0            0.0             48    0.96    

300 -350     325           0            0.0                   48    0.96    

350 -400     375           2      0.4                50    1    

     50    1      

The solution of part (b),(c),(d) and (e) is in attached word file

Step-by-step explanation:

In part a) we take the interval size of 50 and then the resulting 8 classes are  0-50,50-100,100-150,150-200,200-250,250-300,300-350,350-400. The mid points are calculating by adding lower class interval and upper class interval and then dividing it by 2 such as for 1st class 0+50/2=25. The column frequency represents the number of data values occurring in the respective class. Cumulative frequency is computed by adding the frequency of respective class to next class frequency.It remains same for 1st class and for the 2nd class 20+16=36 and so on.  The relative frequency is computed by dividing the frequency by the sum of frequency such as for the 1st class 20/50=0.4 . The cumulative relative frequency is calculated by the same procedure by which the cumulative frequency is calculated.

b)  The frequency histogram is constructed by taking the frequency on y-axis and data set values on x-axis. The resulting histogram is rightly skewed.

c) A frequency polygon is constructed by making the line chart and considering the frequency on y-axis and data set values on x-axis.

d) The relative frequency histogram is constructed by taking the relative frequency on y-axis and data set values on x-axis. The resulting histogram is rightly skewed.

e) An ogive is constructed by making the line chart and considering the cumulative frequency on y-axis and data set values on x-axis.

b

step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (3, - 5) ← 2 points on the line

m = = = - 3

with m = - 3 and (a, b) = (3, - 5), then

y - (- 5) = - 3(x - 3), that is

y + 5 = - 3(x - 3) → b