Question

Find the mean of each distribution.

Answer 1

Answer:

See below ~

Step-by-step explanation:

a)

• Mean = 3(21) + 1(22) + 2(23) + 5(24) + 1(25) / 12
• Mean = 63 + 22 + 46 + 120 + 25 / 12
• Mean = 276/12
• Mean = 23

b)

• Mean = 4.3 + 4.8 + 5.1 + 5.1 + 5.2 + 5.5 + 5.7 + 6.6 + 6.9 + 7.3 + 7.4 / 11
• Mean = 63.9/11
• Mean = 5.81

Answer 2

Answer:

a) 23 °C

b) 5.81 m² (2 dp)

Step-by-step explanation:

Part (a)

This set of data is presented as a Dot Plot.

The frequency (how often a data value occurs) is represented by the number of dots above each data value.

For example, in this dot plot, there are 3 dots above the data value 21 °C and so this means that there are three of this particular data value in the set of data.

To find the mean, we need to multiply each data value by its frequency, add them up, then divide by the total frequency.

$\begin{aligned}\textsf{mean}&=\dfrac{3 \times 21+1 \times 22+2\times 23+5\times 24+1\times 25}{3+1+2+5+1}\\\\ & = \dfrac{63+22+46+120+25}{12}\\\\& = \dfrac{276}{12}\\\\&=23^{\circ} \sf C\end{aligned}$

Part (b)

This set of data is presented as a stem and leaf diagram, where the units and tenths are split.  The units column is the 'stem' and the tenths become the 'leaf'.

Therefore, the first row of this stem and leaf diagram represents 2 data values: 4.3 and 4.8

To find the mean, sum the data values, then divide by the total frequency.

To find the total frequency, simply count the number of values in the leaf part of the diagram.

Data values = 4.3, 4.8, 5.1, 5.1, 5.2, 5.5, 5.7, 6.6, 6.9, 7.3, 7.4

Total frequency = 11

$\begin{aligned}\textsf{mean} &=\dfrac{4.3 + 4.8 + 5.1+5.1+5.2+5.5+5.7+6.6+6.9+7.3+7.4}{11}\\ & = \dfrac{63.9}{11}\\\\& = 5.81\:\textsf{(2 dp)}\end{aligned}$