Chapter 10.2, Problem 11IP

i.

To determine

To find: The city has a greater range of temperature.

Answer to Problem 11IP

Antelope has greater range of temperature,

Explanation of Solution

Given Information: In this table shows average monthly temperature for two different cities.

Antelope MT

Data set: $\{21,24,30,37,42,58,58,70,72,79,84,84\}$

Range: To find the range subtract the lowest value from the highest value.

Range= highest-lowest

= 84-21 = 63

Quartiles: To find the quartiles divide the data set into two values. Don’t include the median if there is an odd number of items.

  $\{21,24,30,37,42,58\}\{58,70,72,79,84,84\}$

The first quartile is the median of the lower half. The first quartile is 33.5

The quartile is the median of the upper half. The third quartile is 75.5.

The interquartile range is the difference between the quartiles.

Interquartile range = 77.5-33.5 = 42.

Outliers: To find any outliers, first multiply the interquartile range by 1.5

  $42\times 1.5=63$

Subtract 63 from the first quartile and add 63 to the third quartiles

  $\begin{array}{l}33.5-63=29.5\\ 75.5+63=138.5\end{array}$

Any value that is less than -29.5 as greater than 138.5 is an outlier.

  $\{21,24,30,37,42,58,58,70,72,79,84,84\}$

There are no outliers.

Augusta,ME

Data set: $\{28,32,34,41,46,53,58,66,70,75,79,80\}$

Range = 80-28 =52

Quartiles $\begin{array}{l}\{28,32,34,41,46,53\}\\ \{58,66,70,75,79,80\}\end{array}$

First quartile = 37.5

Third quartile = 72.5

Interquartile range =72.5-37.5 = 35

Outliers = $35\times 1.5=52.5$

Any value that is less than -15 or greater than 125 is an outlier

  $\{28,32,34,41,46,53,58,66,70,75,79,80\}$

There are no outliers.

We see that Antelope, MT has greater range (63) than augusta ME (52).

ii.

To determine

To find: The measure of variability for each city.

Answer to Problem 11IP

The measures of variability are the quartiles and the inter-quartiles range

Explanation of Solution

Given Information: In this table shows average monthly temperature for two different cities.

The measure of variability are the quartiles and the interquartile range. They are listed above.

iii.

To determine

To find: The median and the interquartile ranges of the average temperature.

Answer to Problem 11IP

Antelope has a median of 58 degree while augusta has a median of 55.5.Antelope has an interquartile range of 42 while augusta is 35.

Explanation of Solution

Given Information: In this table shows average monthly temperature for two different cities.

Antelope has a median of 58 degree while augusta has a median of 55.5.Antelope has an interquartile range of 42 while augusta is 35.

iv.

To determine

To find: The appropriate measure of center to describe the average high temperature for augusta, justify your response.

Answer to Problem 11IP

Augusta average temperature have no outlines, large gaps R and not too money repeated values. The mean is more appropriate.

Explanation of Solution

Given Information: In this table shows average monthly temperature for two different cities.

Augusta average temperature have no outlines, large gaps R and not too money repeated values. The mean is more appropriate.

v.

To determine

To find: The average temperature of antelope and augusta, using both the measure of center and variability.

Answer to Problem 11IP

antelope’s temperature are between 33.5 and 75.5 degree and augusta’s temperatures are between 37.5 and 72.5 degrees.

Explanation of Solution

Given Information: In this table shows average monthly temperature for two different cities.

Antelope one fourth of antelope’s temperature are lower than 33.5 degree. One fourth of antelope is temperature are higher than 75.5 degree. Half of antelope’s temperature are between 33.5 and 75.5 degree.

Augusta: One fourth of augusta temperature are higher than 72.5 degrees. Half of augusta’s temperatures are between 37.5 and 72.5 degrees.