Question

the following data set outlines the scores students had on an algebra test.

1. fill in the frequency table(below)

1. draw a histogram on the graph below by drawing a horizontal line segment the top of each histogram bar. optional: then draw vertical line segments for the sides.

Explanation:

Step1: Count frequencies for each interval

• For \(40 - 49\): Numbers are \(46,45\), so frequency \(= 2\)
• For \(50 - 59\): Numbers are \(57,55,51\), so frequency \(= 3\)
• For \(60 - 69\): Numbers are \(67,65,62,68,63\), so frequency \(= 5\)
• For \(70 - 79\): Numbers are \(70,74,78,73\), so frequency \(= 4\)
• For \(80 - 89\): Numbers are \(80,81,87,88,86\), so frequency \(= 5\)
• For \(90 - 99\): Numbers are \(94,96,93,95,99,90\), so frequency \(= 6\)

Step2: Draw histogram

• On the \(x -\)axis, mark intervals \(40 - 49,50 - 59,\cdots,90 - 99\)
• On the \(y -\)axis, mark frequencies.
• For the interval \(40 - 49\), draw a bar up to \(y = 2\)
• For the interval \(50 - 59\), draw a bar up to \(y = 3\)
• For the interval \(60 - 69\), draw a bar up to \(y = 5\)
• For the interval \(70 - 79\), draw a bar up to \(y = 4\)
• For the interval \(80 - 89\), draw a bar up to \(y = 5\)
• For the interval \(90 - 99\), draw a bar up to \(y = 6\)

Answer:

i) The frequency table is filled as follows:

Score	Frequency
\(50 - 59\)	\(3\)
\(60 - 69\)	\(5\)
\(70 - 79\)	\(4\)
\(80 - 89\)	\(5\)
\(90 - 99\)	\(6\)

ii) The histogram is drawn with bars corresponding to each score interval and their respective frequencies as described in the steps above.