randFromArray([ 5, 6 ])
$.map( new Array( NUM_STUDENTS ), function() { return randRange( 12, 20 ) * 5; } ) $.map( new Array( NUM_STUDENTS ), function() { return randRange( 12, 20 ) * 5; } ) $.map( new Array( NUM_STUDENTS ), function( e, n ) { return FINAL[ n ] - MIDTERM[ n ]; } ) $.map( IMPROVEMENT, function( x ) { return x > 0 ? 1 : null; }).length IMPROVEMENT.slice().sort(function(a,b){return a - b;})[4] === IMPROVEMENT.slice().sort(function(a,b){return a - b;})[3] false
Use the following graph to answer the question below:
init({ range: [ [ -2, NUM_STUDENTS * 3 + 2 ], [ -3, 12 ] ], scale: [ 24, 24 ] }); 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 ); $( 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 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 score, add up the individual scores and divide by the number of students.

\dfrac{plus.apply( null, COLUMN === 0 ? MIDTERM : FINAL )}{NUM_STUDENTS} = \dfrac{sum( COLUMN === 0 ? MIDTERM : FINAL )}{NUM_STUDENTS} = AVERAGE

The average student 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 score on the midterm, add up the individual scores and divide by the number of students.

\dfrac{plus.apply( null, MIDTERM )}{NUM_STUDENTS} = \dfrac{sum( MIDTERM )}{NUM_STUDENTS} = MIDTERM_AVG

The average student 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 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{sum( FINAL )}{NUM_STUDENTS} = FINAL_AVG

The average student score on the final exam was FINAL_AVG.

The average student score was higher on the midterm than on the final exam.

The average student score was higher on the final exam than the midterm.

The average student score was the same on both the midterm and the final exam.

randRange( 0, 1 ) [ "midterm", "final exam" ][ COLUMN ] COLUMN === 0 ? median( MIDTERM ) : median( FINAL )

What was the median score for the TEST?

MEDIAN

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.

\qquad\large{toSentence( COLUMN === 0 ? MIDTERM : FINAL, "" )}

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" }); }

Put the TEST scores in order from least to greatest.

\qquad\large{toSentence( sortNumbers( COLUMN === 0 ? MIDTERM : FINAL ), "" )}

Since there are an odd number of scores, the median score is just the middle score.

Since there are an even number of scores, the median score is the average of the two middle scores.

\dfrac{ COLUMN === 0 ? sortNumbers( MIDTERM )[ NUM_STUDENTS / 2 - 1 ] : sortNumbers( FINAL )[ NUM_STUDENTS / 2 - 1 ] + COLUMN === 0 ? sortNumbers( MIDTERM )[ NUM_STUDENTS / 2 ] : sortNumbers( FINAL )[ NUM_STUDENTS / 2 ] }{2} = MEDIAN

The median score on the TEST was MEDIAN.

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.