91影视

$掳C=\frac{5}{9}掳F鈭�\frac{160}{9}$

Mean, ${渭}_F=77掳F$

Standard deviation,${蟽}_F=3掳F$

Since

$掳C=\frac{5}{9}掳F鈭�\frac{160}{9}$

In order to convert every data value from $掳F$to $掳C$, every data value needs to be multiplied by $\frac{5}{9}$and decreased by $\frac{160}{9}$

Because the mean represents the distribution's center.

When every data value is multiplied by $5/9$then the distribution's center is also multiplied by $\frac{5}{9}$

Similarly,

When every data value is decreased by $\frac{160}{9}$then the distribution's center is likewise reduced by $\frac{160}{9}$

Then

The new mean $掳C$is the mean is$掳F$multiplied by 5/9 and decreased by 160/9

New mean,

$渭C=\frac{5}{9}{渭}_F鈭�\frac{160}{9}=\frac{5}{9}\left(77\right)鈭�\frac{160}{9}=\frac{385}{9}鈭�\frac{160}{9}=\frac{225}{9}=25掳C$

Thus,

The mean temperature reading in degrees Celsius is $25掳C$

Since

$掳C=\frac{5}{9}掳F鈭�\frac{160}{9}$

In order to convert every data value from $掳F$to $掳C$, every data value needs to be multiplied by $\frac{5}{9}$and decreased by $\frac{160}{9}$

Because the standard deviation is a measure of variance.

When every data value is multiplied by 5/9 , then the distribution's variability is likewise multiplied by $\frac{5}{9}$

And

When each data value is reduced by $\frac{160}{9}$ the variability of the distribution remains unchanged.

Then

The new standard deviation in $掳C$is the standard deviation in $掳F$multiplied by $\frac{5}{9}$but not decreased by $\frac{160}{9}$

New standard deviation,

Thus,

${蟽}_C=\frac{5}{9}{蟽}_F=\frac{5}{9}\left(3\right)=\frac{15}{9}=\frac{5}{3}鈮�1.6667掳C$

The standard deviation of the temperature readings in degrees Celsius is $1.6667掳C$