Question

the following four sets of 7 numbers all have a mean of 9. complete parts (a) through (d) below.
{9,9,9,9,9,9,9} , {8,8,9,9,9,10,10} , {6,6,6,9,12,12,12} , {4,4,4,9,14,14,14}

compute the standard deviation for set {6,6,6,9,12,12,12}.
s = 3.0 (round to the nearest tenth as needed.)
compute the standard deviation for set {4,4,4,9,14,14,14}.
s = 5.0 (round to the nearest tenth as needed.)
d. based on your results, briefly explain how the standard deviation provides a useful single - number summary of the variation in these data sets.
the standard deviation is a measure of how widely data values are spread around the of a data set. note that in the fir data set the difference between highest and lowest value is and the standard deviation is 0 and in the last data set the difference between highest and lowest value is than in other data sets and the standard deviation is the

Explanation:

Step1: Recall standard deviation concept

Standard deviation measures spread around the mean of a data set.

Step2: Analyze first data set

First set: \(\{9,9,9,9,9,9,9\}\). Highest - lowest \(= 9 - 9=0\), standard deviation \(= 0\) (since all values are same, no spread).

Step3: Analyze last data set (e.g., \(\{4,4,4,9,14,14,14\}\))

Highest value \( = 14\), lowest \(=4\), difference \(=14 - 4 = 10\). Compare with other sets (e.g., \(\{6,6,6,9,12,12,12\}\) has \(12 - 6=6\)). So last set's range (highest - lowest) is larger than others, and its standard deviation (e.g., \(5.0\)) is larger than others (e.g., \(3.0\) for the \(6,6,6,9,12,12,12\) set).

Answer:

First blank: mean
Second blank: \(0\)
Third blank: larger
Fourth blank: largest

(For the blanks in order: The standard deviation is a measure of how widely data values are spread around the \(\boldsymbol{\text{mean}}\) of a data set. Note that in the first data set the difference between highest and lowest value is \(\boldsymbol{0}\) and the standard deviation is \(0\) and in the last data set the difference between highest and lowest value is \(\boldsymbol{\text{larger}}\) than in other data sets and the standard deviation is the \(\boldsymbol{\text{largest}}\).)