Question

Consider the following data on distances traveled by 100 people to visit the local park.

distance	frequency
1-8	30
9-16	25
17-24	25
25-32	10
33-40	10

Expand and construct the table adding columns for relative frequency and cumulative relative frequency. Then plot Histogram, Frequency Polygon and Ogive Curve.

Answer 1

GIVEN:

The data on distances traveled by 100 people to visit the local park:

Distance	Frequency
1-8	30
9-16	25
17-24	25
25-32	10
33-40	10

SOLUTION:

A relative frequency is the fraction of times an answer occurs. To find the relative frequencies, divide each frequency by the total number of observations in the sample.

Cumulative relative frequency is the accumulation of the previous relative frequencies. To find the cumulative relative frequencies, add all the previous relative frequencies to the relative frequency for the current row.

Distance	Frequency	Relative Frequency	Cumulative Relative Frequency
1-8	30	30/100=0.30	0.30
9-16	25	25/100=0.25	0.30+0.25=0.55
17-24	25	25/100=0.25	0.55+0.25=0.80
25-32	10	10/100=0.10	0.80+0.10=0.90
33-40	10	10/100=0.10	0.90+0.10=1.00
Total	100	1.00	1.00

HISTOGRAM:

FREQUENCY POLYGON:

• Calculate the classmark/midpoint for each class interval. The formula for class mark is:

Classmark = (Upper limit + Lower limit) / 2

• Mark all the class marks on the horizontal axis. It is also known as the mid-value of every class.
• Corresponding to each class mark, plot the frequency as given to you. Make sure that the frequency is plotted against the class mark and not the upper or lower limit of any class.
• Join all the plotted points using a line segment.
• This resulting curve is called the frequency polygon.

Distance	Class mark (Distance)	Frequency
1-8	4.5	30
9-16	12.5	25
17-24	20.5	25
25-32	28.5	10
33-40	36.5	10

OGIVE CURVE:

Draw an x-y graph with percent cumulative relative frequency on the y-axis (from 0 to 100%). Mark the x-axis with the class boundaries.

Plot the points. Each point should be plotted on the upper limit of the class boundary. For example, if the first class boundary is 0 to 10, the point should be plotted at 10.

Connect the dots with straight lines. the ogive is one continuous line, made up of several smaller lines that connect pairs of dots, moving from left to right.

Distance	Cumulative Relative Frequency	Percent Cumulative Relative Frequency
1-8	0.30	30%
9-16	0.30+0.25=0.55	55%
17-24	0.55+0.25=0.80	80%
25-32	0.80+0.10=0.90	90%
33-40	0.90+0.10=1.00	100%