Question

The approximate mean age is years.(Round to one decimal place as needed.)Approximate the mean of the frequency distribution for the ages of the residents of a town.Age0-910-1920-2930-3940-4950-5960-6970-7980-89Frequency32351228246043173

Answer 1

To calculate the mean value of a data set displayed on a frequency table you have to use the following formula:

$X_{\text{bar}}=\frac{\Sigma x^{\prime}fi}{n}$

Where

Xbar is the mean value

x' is the classmark (or midpoint) of each interval

fi is the observed frequency of each interval

n is the sample size.

To determine the sample size you have to add the observed frequencies of all intervals:

$\begin{gathered} n=\Sigma fi \\ n=32+35+12+28+24+60+43+17+3 \\ n=254 \end{gathered}$

To determine the classmark of each interval you have to add the upper bond and the lower bond and divide it by 2

$x^{\prime}=\frac{\text{upperbond}+\text{lowerbond}}{2}$

First interval (0-9)

$\begin{gathered} x^{\prime}=\frac{9+0}{2} \\ x^{\prime}=4.5 \end{gathered}$

Second interval (10-19)

$\begin{gathered} x^{\prime}=\frac{19+10}{2} \\ x^{\prime}=14.5 \end{gathered}$

Third interval (20-29)

$\begin{gathered} x^{\prime}=\frac{29+20}{2} \\ x^{\prime}=24.5 \end{gathered}$

Fourth interval (30-39)

$\begin{gathered} x^{\prime}=\frac{30+39}{2} \\ x^{\prime}=34.5 \end{gathered}$

Fifth interval (40-49)

$\begin{gathered} x^{\prime}=\frac{49+40}{2} \\ x^{\prime}=44.5 \end{gathered}$

Sixth interval (50-59)

$\begin{gathered} x^{\prime}=\frac{59+50}{2} \\ x^{\prime}=54.5 \end{gathered}$

Seventh interval (60-69)

$\begin{gathered} x^{\prime}=\frac{69+60}{2} \\ x^{\prime}=64.5 \end{gathered}$

Eighth interval (70-79)

$\begin{gathered} x^{\prime}=\frac{79+70}{2} \\ x^{\prime}=74.5 \end{gathered}$

Ninth interval (80-89)

$\begin{gathered} x^{\prime}=\frac{89+80}{2} \\ x^{\prime}=84.5 \end{gathered}$

Next is to multiply each classmark by the frequency of the corresponding interval:

Once you've multiplied each classmark by each frequency and added all results, you can calculate the mean value using the formula:

$\begin{gathered} X_{\text{bar}}=\frac{∑x^{\prime}fi}{n} \\ X_{\text{bar}}=\frac{10543}{254} \\ X_{\text{bar}}=41.507\approx41.5 \end{gathered}$

The average or mean age of the resident of the town is 41.5 years