Question

Find the mean for the following frequency tables

Short answer

$$\begin{gathered} \text{Meanofgrade}=79.5 \\ \text{Meanofdailylowtemperature}=60.9356 \\ \text{Meanofpointspergame}=70.6628 \end{gathered}$$

Step-by-step solution

Given information

Given the frequency tables.

Explanation

Grade
LCB	UCB	Mid point (x)	Frequency (f)	$x\times f$
49.5	59.5	54.5	2	109
59.5	6.95	64.5	3	193.5
69.5	79.5	74.5	8	596
79.5	89.5	84.5	12	1014
89.5	99.5	94.5	5	472.5
		Total	30	2385

So mean of grade is

$\frac{{\sum }_{i=1}^5{x}^{*}f}{{\sum }_{i=1}^{5}f}=\frac{2385}{30}=79.5$

Daily low temperature
LCB	UCB	Mid point (x)	Frequency (f)	$x\times f$
49.5	59.5	54.5	53	2888.5
59.5	69.5	64.5	32	2064
69.5	79.5	74.5	15	1117.5
79.5	89.5	84.5	1	84.5
89.5	99.5	94.5	0	0
		Total	101	6154.50

So mean of Daily low temperature is

$\frac{{\sum }_{i=1}^5{x}^{*}f}{{\sum }_{i=1}^{5}f}=\frac{6154.5}{101}=60.9356$

Points per Game
LCB	UCB	Mid point (x)	Frequency (f)	$x\times f$
49.5	59.5	54.5	14	763
59.5	69.5	64.5	32	2064
69.5	79.5	74.5	15	1117.5
79.5	89.5	84.5	23	1943.5
89.5	99.5	94.5	2	189
		Total	86	6077

So mean of points per game is$\frac{{\sum }_{i=1}^5{x}^{*}f}{{\sum }_{i=1}^{5}f}=\frac{6077}{86}=70.6628$