Question

Ethan and Drew went on a 10-day fishing trip. The number of smallmouth bass caught and released by the two boys each day is shown in the accompanying data table. Complete parts (a) through (d) below. Click the icon to view the data table. (a) Find the population mean and the range for the number of smallmouth bass caught per day by each fisherman. Do these values indicate any differences between the two fishermen's catches per day? The range for the number of smallmouth bass caught per day by Ethan is (Type an integer or a decimal. Do not round.) The population mean for the number of smallmouth bass caught per day by Ethan is (Simplify your answer.) The range for the number of smallmouth bass caught per day by Drew is . (Type an integer or a decimal. Do not round.) The population mean for the number of smallmouth bass caught per day by Drew is - (Simplify your answer.) Do these values indicate any differences between the two fishermen's catches per day? A. Yes. Ethan has a much lower population mean than Drew. B. No. Both Ethan and Drew have a similar range. OC. No. Both Ethan and Drew have a similar population mean and range. D. Yes. Ethan has a much higher range than Drew. (b) Draw a dot plot for Ethan. Draw a dot plot for Drew. Which fisherman seems more consistent? سلملمحطلهعمللعلوم Choose the correct dot 1 Click here to view Data Table Click here to view Click here to views Click here to view Choose the correct dot 0 9 8 Ethan Drew 8 15 24 2 9 3 5 20 9 17 10 2 8 19 10 3 18 Print Done Click here to view Click here to view Click here to view dot plot d O Click here to view dot plot Which fisherman seems more consistent? A. Ethan seems more consistent, since his observations are spread out. B. Ethan seems more consistent, since more of his observations are clustered together. C. Drew seems more consistent, since his observations are spread out. D. Drew seems more consistent, since more of his observations are clustered together. (c) Find the population standard deviation for the number of smallmouth bass caught per day by each fisherman. Do these values present a different story about the two fishermen's catches per day? Which fisherman has the more consistent record? The population standard deviation for the number of smallmouth bass caught per day by Ethan is . (Round to one decimal place as needed.) The population standard deviation for the number of smallmouth bass caught per day by Drew is (Round to one decimal place as needed.) Do these values present a different story about the two fishermen's catches per day? since the fishermen have population means and ranges while having population standard deviations, Which fisherman has the more consistent record?

Answer 1

Note: Final answers are highlighted in colour.

a)

	Ethan	Formula_1	Drew	Formula_2
	8		15
	24		2
	9		3
	9		18
	5		20
	8		1
	9		17
	10		2
	8		19
	10		3
Min	5	MIN(B2:B11)	1	MIN(C2:C11)
Max	24	MAX(B2:B11)	20	MAX(C2:C11)
Population mean	10	AVERAGE(B2:B11)	10	AVERAGE(C2:C11)

From the above table,

The range for the number of smallmouth bass caught per day by Ethan=  Max- Min= 24-5 = 19

The population mean for the number of smallmouth bass caught per day by Ethan=10

The range for the number of smallmouth bass caught per day by Drew= Max- Min= 20-1= 19

The population mean for the number of smallmouth bass caught per day by Drew=10

Do these values indicate any differences between the two fisherman's catches per day?

No, Both Ethan and Drew have a similar population mean and range (Option C)

b) Making a dotplot

Step 1: Create a new column beside our data column, and type the formula COUNTIF($A$2:$A2,A2) in the first cell of the new column.

2 Clipboard Font B2 for =COUNTIF($A$2:$A2,A2) A B с D E F 1 Ethan 2 8 3 24 1! 1 1 2 4 9 Сл 9 6 5 1 7 8 2 8 9 3 9 10 1 8 3 10 11 10 2

Step2: Copy the fomula into other cells of the column.

Step3: Select the data , go to Insert>> Recommended charts and select Scatter and click on Ok.

File Home Insert Draw Page Layout Formulas Data Review View Developer Help Get Add-ins b? L Illustrations Pivot Table Recommended Table Pivot Tables My Add-ins Recommended Charts Maps PivotChart 3D Map y Tables Add-ins Charts Tours A1 х Insert Chart ? Х A B Recommended Charts All Charts 1 Ethan 2 Scatter 00 1 3 24 1 4 9 1 3.5 . 5 9 2 3 6 5 1 2.5 7 8 2 Charte 8 9 3 2 9 10 1 LLا 1.5 10 00 3 JULT. 1 11 LO 2 0.5 Title 12 13 0 0 5 10 15 20 25 30 14 15 A scatter chart is used to compare at least two sets of values or pairs of data. Use it to show relationships between sets of values. 16 17 Dhart Title 18 - 19 20 OK Cancel 21

This will give the below Dot plot for Ethan

3.5 3 Lл N 1.5 1 . 0.5 0 л 0 10 15 20 25 30

Similarly ,Dot plot for Drew is

2.5 N in 1 0. in 0 0 5 10 15 20 25

The clustered dotplot indicates the consistency of the data.

Which fisherman seems more consistent?

Ethan seems more consistent ,since more of his observations are clustterd together. (Option B)

c)

The population standard deviation for the number of smallmouth bass caught per day by Ethan=STDEV.P(B2:B11)=4.9

The population standard deviation for the number of smallmouth bass caught per day by Drew=STDEV.P(C2:C11)=7.9

Do these values present a different story about the two fisherman’s catches per day?

Yes since the fishermen have same population means and ranges while having different population standard deviations.

Which fisherman has the more consistent record?

Ethan has the more consistent record, since his standard deviation is lower.(Option B)

d) Discuss limitations of the range as a measure of dispersion

The range only takes into account the smallest and the largest values, which does not provide any information about the dispersion of the distribution between those values. (Option D)