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Aussie, Aussie, Aussie A group of Australian students were asked to estimate the width of their classroom in feet. Use the dot plot and summary statistics to answer the following questions.

a. Suppose we converted each student鈥檚 guess from feet to meters (3.28 ft=1 m ). How would the shape of the distribution be affected? Find the mean,

median, standard deviation, and IQR for the transformed data.

b. The actual width of the room was 42.6 feet. Suppose we calculated the error in each student鈥檚 guess as follows: guess 鈭 42.6. Find the mean and standard deviation of the errors in feet.

c. Find the percentile for the student who estimated the classroom width as 63 feet.

Short Answer

Expert verified

Part (a)x=13.3232Median=12.8049s=3.8110IQR=2.5915

Part (b) x=1.1s=12.50

Part (c) 92nd percentile

Step by step solution

01

Part (a) Step 1: Given information

x=43.70MEDIN=42.00s=12.50Q1=35.50Q3=44.00

02

Part (a) Step 2: Concept

Percentile=Numberofdatavaluesthatarelessthantheindividual'sdatavalueTotalnumberofdatavalues100%

03

Part (a) Step 3: Calculation

Relationship between feet and meter:

3.2ft=1m1ft=13.28m

The difference between the third and first quartiles is the interquartile range:

IQR=Q3Q1=44.0035.50=8.50

To convert the measurement from feet to meters, multiply by 3.28:

x=43.703.28=13.3232MEDIAN=42.003.28=12.8049s=12.503.28=3.8110IQR=8.503.28=2.5915

The distribution's shape would not be modified because every data value is translated in the same way, and so the data values would be distributed in the same way.

04

Part (b) Step 1: Calculation

Every guess reduced the error distribution by 42.6 percent. Then the mean goes down by the same amount:

x=43.7042.60=1.1

Because the spread would not vary when the value reduced by the same amount, the standard deviation would remain unchanged.

s=12.50

05

Part (c) Step 1: Calculation

The summary statistic has a value of 66below n, indicating that there are 66data values in the data set.

4dots are to the right of 63on the dot plot, and 1 dot is related with 63implying that 66-4-1=61dots of the 66dots are to the left of 63

Required percentile

Percentile=Numberofdatavaluesthatarelessthantheindividual'sdatavalueTotalnumberofdatavalues100%

=6166100%=0.92100%=92%

Therefore the percentile associated with 63feet is the 92ndpercentile.

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