Commercial dredging operations in ancient rivers occasionally uncover archaeological artifacts of great importance. One such artifact is Bronze Age spearheads recovered from ancient rivers in Ireland. A recent study gave the following information regarding discoveries of ancient bronze spearheads in Irish rivers.

Rivers Bann Blackwater Erne Shannon Barrow
No of spearheads 25 7 15 33 14

a. Make the photo chart for these data.
b. Make the cricle chart for these data.

(a) Pareto Chart attached as a picture

(b) Circle chart attached as a picture

Step-by-step explanation:

Rivers                     Bann   Blackwater   Erne   Shannon   Barrow

No of spearheads    25           7                15          33            14

The question is asking to make a Pareto chart in the first part and a circle chart in the second part.

(a) To compute the Pareto chart, we need to plot the no. of spearheads in descending order starting from the highest i.e. River Shannon. A descending bar graph would be plotted.

We also need to plot a line which shows the cumulative percentage of the data at each both. To compute the cumulative percentage, first we need to compute the individual percentage at each point and then add them up at every step to compute the cumulative percentage. The data can be first arranged in a descending order and then all the computations can be made to plot the graph easily.

Rivers            No. of Spearheads                Percentage          Cumulative %

Shannon                      33                       (33/94)*100= 35.1%          35.1%

Bann                            25                       (25/94)*100= 26.6%         61.7%

Erne                             15                        (15/94)*100= 16.0%           77.7%

Barrow                         14                        (14/94)*100= 14.9%           92.6%

Blackwater                   7                         (7/94)*100= 7.4%               100%

The cumulative % is plotted as a line while the no. of spearheads are plotted as a bar graph. The Pareto plot is attached as an image. I have plotted it on excel.

(b) To make a circle chart for this data, we need to compute the angles for each river. To compute the angles, the following formula will be used:

Angle = (No. of spearheads/total no. of spearheads) * 360

Angle(Bann) = (25/94) * 360 = 95.7°

Angle(Blackwater) = (7/94) * 360 = 26.8°

Angle(Erne) = (15/94) * 360 = 57.4°

Angle(Shannon) = (33/94) * 360 = 126.4°

Angle(Barrow) = (14/94) * 360 = 53.6°

The angles are plotted inside a circle to make a circle chart. I am attaching the circle chart as a picture.

5/12, or 5: 12

step-by-step explanation: