Consider the following data on two categorical variables. The first variable, x, can take on values A, B, C, or D. The second variable, y, can take on values I or II. The following table gives the frequency with which each combination occurs. x y I II A 163 837 B 190 810 C 301 699 D 410 590 (a) Construct a side-by-side bar chart with x on the horizontal axis. A side-by-side bar chart is given. The horizontal axis has no label. The vertical axis is labeled Frequency. There are 4 groups of bars with labels A, B, C, and D. Each group contains two bars one bar labeled I and one bar labeled II. In group A the bar labeled I is 837 units tall and the bar labeled II is 163 units tall. In group B the bar labeled I is 810 units tall and the bar labeled II is 190 units tall. In group C the bar labeled I is 699 units tall and the bar labeled II is 301 units tall. In group D the bar labeled I is 590 units tall and the bar labeled II is 410 units tall. A side-by-side bar chart is given. The horizontal axis has no label. The vertical axis is labeled Frequency. There are 4 groups of bars with labels A, B, C, and D. Each group contains two bars one bar labeled I and one bar labeled II. In group A the bar labeled I is 163 units tall and the bar labeled II is 337 units tall. In group B the bar labeled I is 190 units tall and the bar labeled II is 310 units tall. In group C the bar labeled I is 301 units tall and the bar labeled II is 199 units tall. In group D the bar labeled I is 410 units tall and the bar labeled II is 90 units tall. A side-by-side bar chart is given. The horizontal axis has no label. The vertical axis is labeled Frequency. There are 4 groups of bars with labels A, B, C, and D. Each group contains two bars one bar labeled I and one bar labeled II. In group A the bar labeled I is 337 units tall and the bar labeled II is 163 units tall. In group B the bar labeled I is 310 units tall and the bar labeled II is 190 units tall. In group C the bar labeled I is 199 units tall and the bar labeled II is 301 units tall. In group D the bar labeled I is 90 units tall and the bar labeled II is 410 units tall. A side-by-side bar chart is given. The horizontal axis has no label. The vertical axis is labeled Frequency. There are 4 groups of bars with labels A, B, C, and D. Each group contains two bars one bar labeled I and one bar labeled II. In group A the bar labeled I is 163 units tall and the bar labeled II is 837 units tall. In group B the bar labeled I is 190 units tall and the bar labeled II is 810 units tall. In group C the bar labeled I is 301 units tall and the bar labeled II is 699 units tall. In group D the bar labeled I is 410 units tall and the bar labeled II is 590 units tall. (b) Comment on the relationship between x and y. As x goes from A to D, the frequency for I  ---Select--- decreases increases and the frequency of II  ---Select--- increases decreases .

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Consider the following data on two categorical variables. The first variable, x, can take on values A, B, C, or D. The second variable, y, can take on values I or II. The following table gives the frequency with which each combination occurs.
x y
I II
A 163 837
B 190 810
C 301 699
D 410 590
(a)
Construct a side-by-side bar chart with x on the horizontal axis.
A side-by-side bar chart is given. The horizontal axis has no label. The vertical axis is labeled Frequency. There are 4 groups of bars with labels A, B, C, and D. Each group contains two bars one bar labeled I and one bar labeled II.
  • In group A the bar labeled I is 837 units tall and the bar labeled II is 163 units tall.
  • In group B the bar labeled I is 810 units tall and the bar labeled II is 190 units tall.
  • In group C the bar labeled I is 699 units tall and the bar labeled II is 301 units tall.
  • In group D the bar labeled I is 590 units tall and the bar labeled II is 410 units tall.
A side-by-side bar chart is given. The horizontal axis has no label. The vertical axis is labeled Frequency. There are 4 groups of bars with labels A, B, C, and D. Each group contains two bars one bar labeled I and one bar labeled II.
  • In group A the bar labeled I is 163 units tall and the bar labeled II is 337 units tall.
  • In group B the bar labeled I is 190 units tall and the bar labeled II is 310 units tall.
  • In group C the bar labeled I is 301 units tall and the bar labeled II is 199 units tall.
  • In group D the bar labeled I is 410 units tall and the bar labeled II is 90 units tall.
A side-by-side bar chart is given. The horizontal axis has no label. The vertical axis is labeled Frequency. There are 4 groups of bars with labels A, B, C, and D. Each group contains two bars one bar labeled I and one bar labeled II.
  • In group A the bar labeled I is 337 units tall and the bar labeled II is 163 units tall.
  • In group B the bar labeled I is 310 units tall and the bar labeled II is 190 units tall.
  • In group C the bar labeled I is 199 units tall and the bar labeled II is 301 units tall.
  • In group D the bar labeled I is 90 units tall and the bar labeled II is 410 units tall.
A side-by-side bar chart is given. The horizontal axis has no label. The vertical axis is labeled Frequency. There are 4 groups of bars with labels A, B, C, and D. Each group contains two bars one bar labeled I and one bar labeled II.
  • In group A the bar labeled I is 163 units tall and the bar labeled II is 837 units tall.
  • In group B the bar labeled I is 190 units tall and the bar labeled II is 810 units tall.
  • In group C the bar labeled I is 301 units tall and the bar labeled II is 699 units tall.
  • In group D the bar labeled I is 410 units tall and the bar labeled II is 590 units tall.
(b)
Comment on the relationship between x and y.
As x goes from A to D, the frequency for I  ---Select--- decreases increases and the frequency of II  ---Select--- increases decreases .
 
 

 

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