Answer:
a) 4.60 (2 dp)
b) 1.31 (2 dp)
c) 8.8
Step-by-step explanation:
The "Frequency" part of a frequency table is the measure of how often the data value occurs.
To calculate the mean of data presented in a frequency table, we need to multiply each data value by its given frequency, sum these, then divide by the sum of the frequency.
The formula for mean is:
[tex]\textsf{mean}=\overline{x}=\dfrac{\displaystyle \sum fx}{\displaystyle\sum f}[/tex]
Part (a)
Add a row showing the values of [tex]fx[/tex]
Add a column showing the totals of [tex]f[/tex] and [tex]fx[/tex]
[tex]\large\begin{array}{| c | c | c | c | c | c | c | c |}\cline{1-8} & & & & & & & \sf Total \\\cline{1-8} x & 2 & 3 & 4 & 5 & 6 & 7 & \\\cline{1-8} \textsf{Frequency}\:f & 11 & 17 & 24 & 23 & 18 & 15 & 108\\\cline{1-8} fx & 22 & 51 & 96 & 115& 108 & 105 &497 \\\cline{1-8}\end{array}[/tex]
Now use the formula to calculate the mean:
[tex]\implies \textsf{mean}=\overline{x}=\dfrac{497}{108}=4.60\:\textsf{(2 dp)}[/tex]
Part (b)
Add a column showing the values of [tex]fx[/tex]
Add a row showing the totals of [tex]f[/tex] and [tex]fx[/tex]
[tex]\large\begin{array}{| c | c | c |}\cline{1-3} x & \textsf{Frequency}\: f & fx \\\cline{1-3} 0 & 35 & 0 \\\cline{1-3} 1 & 76 & 76\\\cline{1-3} 2 & 48 & 96\\\cline{1-3} 3 & 22 & 66 \\\cline{1-3} \sf Total & 181 & 238 \\\cline{1-3}\end{array}[/tex]
Now use the formula to calculate the mean:
[tex]\implies \textsf{mean}=\overline{x}=\dfrac{238}{181}=1.31\:\textsf{(2 dp)}[/tex]
Part (c)
Add a column showing the values of [tex]fx[/tex]
Add a row showing the totals of [tex]f[/tex] and [tex]fx[/tex]
[tex]\large\begin{array}{| c | c | c |}\cline{1-3} x & \textsf{Tally}\: f & fx \\\cline{1-3} 8 & 7 & 56\\\cline{1-3} 9 & 10 & 90\\\cline{1-3} 10 & 3 & 30\\\cline{1-3} \sf Total & 20 & 176\\\cline{1-3}\end{array}[/tex]
Now use the formula to calculate the mean:
[tex]\implies \textsf{mean}=\overline{x}=\dfrac{176}{20}=8.8[/tex]
