Question

Find the mean of x of each distribution.

Answer 1

Answer:

See below ~

Step-by-step explanation:

a)

• Mean = 2(11) + 3(17) + 4(24) + 5(23) + 6(18) + 7(15) / 108
• Mean = 22 + 51 + 96 + 115 + 108 + 105 / 108
• Mean = 497 / 108
• Mean = 4.6

b)

• Mean = 0(35) + 1(76) + 2(48) + 3(22) / 181
• Mean = 76 + 96 + 66 / 181
• Mean = 1.31

c)

• Mean = 8(7) + 9(10) + 10(3) / 20
• Mean = 56 + 90 + 30 / 20
• Mean = 176/20
• Mean = 8.8

Answer 2

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:

$\textsf{mean}=\overline{x}=\dfrac{\displaystyle \sum fx}{\displaystyle\sum f}$

Part (a)

Add a row showing the values of $fx$

Add a column showing the totals of $f$ and $fx$

$\large\begin{array}{| c | c | c | c | c | c | c | c |}\cline{1-8} & & & & & & & \sf Total \\\cline{1-8} x & 2 & 3 & 4 & 5 & 6 & 7 & \\\cline{1-8} \textsf{Frequency}\:f & 11 & 17 & 24 & 23 & 18 & 15 & 108\\\cline{1-8} fx & 22 & 51 & 96 & 115& 108 & 105 &497 \\\cline{1-8}\end{array}$

Now use the formula to calculate the mean:

$\implies \textsf{mean}=\overline{x}=\dfrac{497}{108}=4.60\:\textsf{(2 dp)}$

Part (b)

Add a column showing the values of $fx$

Add a row showing the totals of $f$ and $fx$

$\large\begin{array}{| c | c | c |}\cline{1-3} x & \textsf{Frequency}\: f & fx \\\cline{1-3} 0 & 35 & 0 \\\cline{1-3} 1 & 76 & 76\\\cline{1-3} 2 & 48 & 96\\\cline{1-3} 3 & 22 & 66 \\\cline{1-3} \sf Total & 181 & 238 \\\cline{1-3}\end{array}$

Now use the formula to calculate the mean:

$\implies \textsf{mean}=\overline{x}=\dfrac{238}{181}=1.31\:\textsf{(2 dp)}$

Part (c)

Add a column showing the values of $fx$

Add a row showing the totals of $f$ and $fx$

$\large\begin{array}{| c | c | c |}\cline{1-3} x & \textsf{Tally}\: f & fx \\\cline{1-3} 8 & 7 & 56\\\cline{1-3} 9 & 10 & 90\\\cline{1-3} 10 & 3 & 30\\\cline{1-3} \sf Total & 20 & 176\\\cline{1-3}\end{array}$

Now use the formula to calculate the mean:

$\implies \textsf{mean}=\overline{x}=\dfrac{176}{20}=8.8$