Use the following graph to answer the question below:
init({
range: [ [ -2, NUM_STUDENTS * 3 + 2 ], [ -3, 12 ] ],
scale: [ 26, 26 ]
});
for ( var y = 1; y <= 10; ++y ) {
label( [ 0, y ], y * 10, "left", false );
style({ stroke: "#000", strokeWidth: 1, opacity: 0.2 }, function() {
line( [ 0, y ], [ NUM_STUDENTS * 3 + 1, y ] )
});
}
for ( var index = 0; index < NUM_STUDENTS; ++index ) {
style({ stroke: "none", fill: "#9ab8ed", opacity: 1.0 });
path([ [ index * 3 + 1, 0 ], [ index * 3 + 1, MIDTERM[ index ] / 10 ], [ index * 3 + 2, MIDTERM[ index ] / 10 ], [ index * 3 + 2, 0 ], [ index * 3 + 1, 0 ] ]);
style({ stroke: "none", fill: "#ffc966", opacity: 1.0 });
path([ [ index * 3 + 2, 0 ], [ index * 3 + 2, FINAL[ index ] / 10 ], [ index * 3 + 3, FINAL[ index ] / 10 ], [ index * 3 + 3, 0 ], [ index * 3 + 2, 0 ] ]);
style({ opacity: 1.0 });
label( [ index * 3 + 2, 0 ], person( index + 1 ), "below", false );
}
style({ stroke: "#000", strokeWidth: 2, opacity: 1.0 });
line( [ 0, 0 ], [ NUM_STUDENTS * 3 + 1, 0 ] );
line( [ 0, 0 ], [ 0, 10 ] );
label( [ ( NUM_STUDENTS * 3 + 1 ) / 2, -0.8 ], "<b>Student</b>", "below", false );
jQuery( label( [ -1.5, 5 ], "<b>Score (points)</b>", "center", false ) ).addClass( "rotate" );
label( [ ( NUM_STUDENTS * 3 + 1 ) / 2, 10.5 ], "<b>Scores on Midterm and Final Exams</b>", "above", false );
style({ stroke: "none", fill: "#9ab8ed", opacity: 1.0 });
path([ [ 0, -2 ], [ 0.5, -2 ], [ 0.5, -2.5 ], [ 0, -2.5 ], [ 0, -2 ] ]);
style({ stroke: "#000", strokeWidth: 2, opacity: 1.0 });
label( [ 0.5, -2.25 ], "Midterm", "right", false );
style({ stroke: "none", fill: "#ffc966", opacity: 1.0 });
path([ [ 3, -2 ], [ 3.5, -2 ], [ 3.5, -2.5 ], [ 3, -2.5 ], [ 3, -2 ] ]);
style({ stroke: "#000", strokeWidth: 2, opacity: 1.0 });
label( [ 3.5, -2.25 ], "Final", "right", false );
randRange( 0, 1 )
[ "midterm", "final exam" ][ COLUMN ]
COLUMN === 0 ? mean( MIDTERM ) : mean( FINAL )
What was the average student's score for the TEST?
AVERAGE
Use the key to figure out which of the two bars shows the scores for the TEST.
style({ stroke: PINK, fill: "none", strokeWidth: 2 });
ellipse( [ COLUMN * 3 + 1.2, -2.25 ], [ 1.5, 0.5 ] );
Find each of the TEST scores represented by the blueorange bars.
if ( COLUMN === 0 ) {
label( [ INDEX * 3 + 1.5, MIDTERM[ INDEX ] / 10 + 0.2 ], MIDTERM[ INDEX ], "below", false ).css({ fontWeight: "bold" });
} else {
label( [ INDEX * 3 + 2.5, FINAL[ INDEX ] / 10 + 0.2 ], FINAL[ INDEX ], "below", false ).css({ fontWeight: "bold" });
}
To find the average student's score, add up the individual scores and divide by the number of students.
\dfrac{plus.apply( null, COLUMN === 0 ? MIDTERM : FINAL )}{NUM_STUDENTS} =
\dfrac{COLUMN === 0 ? eval( MIDTERM.join( "+" ) ) : eval( FINAL.join( "+" ) )}{NUM_STUDENTS} =
AVERAGE
The average student's score on the TEST was AVERAGE.
true
mean( MIDTERM )
mean( FINAL )
MIDTERM_AVG > FINAL_AVG ? "Midterm" : ( MIDTERM_AVG < FINAL_AVG ? "Final exam" : "Same on both" )
On average, did the students do better on the midterm or the final exam?
ANSWER
- Midterm
- Final exam
- Same on both
Find each of the midterm scores represented by the blue bars.
label( [ INDEX * 3 + 1.5, MIDTERM[ INDEX ] / 10 + 0.2 ], MIDTERM[ INDEX ], "below", false ).css({ fontWeight: "bold" });
To find the average student's score on the midterm, add up the individual scores and divide by the number of students.
\dfrac{plus.apply( null, MIDTERM )}{NUM_STUDENTS} =
\dfrac{eval( MIDTERM.join( "+" ) )}{NUM_STUDENTS} =
MIDTERM_AVG
The average student's score on the midterm was MIDTERM_AVG.
Find each of the final exam scores represented by the orange bars.
label( [ INDEX * 3 + 2.5, FINAL[ INDEX ] / 10 + 0.2 ], FINAL[ INDEX ], "below", false ).css({ fontWeight: "bold" });
To find the average student's score on the final exam, add up the individual scores and divide by the number of students.
\dfrac{plus.apply( null, FINAL )}{NUM_STUDENTS} =
\dfrac{eval( FINAL.join( "+" ) )}{NUM_STUDENTS} =
FINAL_AVG
The average student's score on the final exam was FINAL_AVG.
The average student's score was higher on the midterm
than on the final exam.
The average student's score was higher on the final exam
than the midterm.
The average student's score was the same on both the midterm
and the final exam.
randRange( 0, 1 )
[ "midterm", "final exam" ][ COLUMN ]
COLUMN === 0 ? mode( MIDTERM ) : mode( FINAL )
What was the mode for the TEST scores?
MODE
Use the key to figure out which of the two bars shows the scores for the TEST.
style({ stroke: PINK, fill: "none", strokeWidth: 2 });
ellipse( [ COLUMN * 3 + 1.2, -2.25 ], [ 1.5, 0.5 ] );
Find each of the TEST scores represented by the blueorange bars.
if ( COLUMN === 0 ) {
label( [ INDEX * 3 + 1.5, MIDTERM[ INDEX ] / 10 + 0.2 ], MIDTERM[ INDEX ], "below", false ).css({ fontWeight: "bold" });
} else {
label( [ INDEX * 3 + 2.5, FINAL[ INDEX ] / 10 + 0.2 ], FINAL[ INDEX ], "below", false ).css({ fontWeight: "bold" });
}
The mode is the most frequently occurring score.
MODE is the most frequently occurring score.
if ( COLUMN === 0 ) {
if ( MIDTERM[ INDEX ] === MODE ) {
ellipse( [ INDEX * 3 + 1.5, MIDTERM[ INDEX ] / 10 - 0.5 ], [ 0.8, 0.6 ] );
}
} else {
if ( FINAL[ INDEX ] === MODE ) {
ellipse( [ INDEX * 3 + 2.5, FINAL[ INDEX ] / 10 - 0.5 ], [ 0.8, 0.6 ] );
}
}
randRange( 0, 1 )
[ "midterm", "final exam" ][ COLUMN ]
COLUMN === 0 ? Math.min.apply( null, MIDTERM ) : Math.min.apply( null, FINAL )
COLUMN === 0 ? Math.max.apply( null, MIDTERM ) : Math.max.apply( null, FINAL )
MAX - MIN
What is the range of the TEST scores?
RANGE
The range is the difference between the largest value and the smallest value.
Use the key to figure out which of the two bars shows the scores for the TEST.
style({ stroke: PINK, fill: "none", strokeWidth: 2 });
ellipse( [ COLUMN * 3 + 1.2, -2.25 ], [ 1.5, 0.5 ] );
Find the largest and smallest TEST scores represented by the blueorange bars.
if ( COLUMN === 0 ) {
if ( MIDTERM[ INDEX ] === MIN || MIDTERM[ INDEX ] === MAX ) {
label( [ INDEX * 3 + 1.5, MIDTERM[ INDEX ] / 10 + 0.2 ], MIDTERM[ INDEX ], "below", false ).css({ fontWeight: "bold" });
}
} else {
if ( FINAL[ INDEX ] === MIN || FINAL[ INDEX ] === MAX ) {
label( [ INDEX * 3 + 2.5, FINAL[ INDEX ] / 10 + 0.2 ], FINAL[ INDEX ], "below", false ).css({ fontWeight: "bold" });
}
}
The smallest TEST score is MIN. The largest TEST score is MAX.
Find the range by subtracting the smallest score from the largest score.
\qquad MAX - MIN = RANGE
The range of TEST scores is RANGE.
randRange( 0, 1 )
[ "midterm", "final exam" ][ COLUMN ]
COLUMN === 0 ? Math.min.apply( null, MIDTERM ) : Math.min.apply( null, FINAL )
COLUMN === 0 ? Math.max.apply( null, MIDTERM ) : Math.max.apply( null, FINAL )
(MAX + MIN) / 2
What is the midrange of the TEST scores?
MIDRANGE
The midrange is halfway between the largest value and the smallest value.
Use the key to figure out which of the two bars shows the scores for the TEST.
style({ stroke: PINK, fill: "none", strokeWidth: 2 });
ellipse( [ COLUMN * 3 + 1.2, -2.25 ], [ 1.5, 0.5 ] );
Find the largest and smallest TEST scores represented by the blueorange bars.
if ( COLUMN === 0 ) {
if ( MIDTERM[ INDEX ] === MIN || MIDTERM[ INDEX ] === MAX ) {
label( [ INDEX * 3 + 1.5, MIDTERM[ INDEX ] / 10 + 0.2 ], MIDTERM[ INDEX ], "below", false ).css({ fontWeight: "bold" });
}
} else {
if ( FINAL[ INDEX ] === MIN || FINAL[ INDEX ] === MAX ) {
label( [ INDEX * 3 + 2.5, FINAL[ INDEX ] / 10 + 0.2 ], FINAL[ INDEX ], "below", false ).css({ fontWeight: "bold" });
}
}
The smallest TEST score is MIN. The largest TEST score is MAX.
Find the midrange by averaging the smallest and largest scores.
\qquad \dfrac{MIN + MAX}{2} = MIDRANGE
The midrange of TEST scores is MIDRANGE.