The Association of Business Executives Certificate

x^2	fx^2
		(number of	X	F	fx
		books)
		210 to 219	214.5	7	1,502	46,010	322,072
		220 to 229	224.5	10	2,245	50,400	504,000
		230 to 239	234.5	12	2,814	54,990	659,883
		240 to 249	244.5	7	1,712	59,780	418,462
		250 to 259	254.5	4	1,018	64,770	259,081
		40 9,310	2,172,800	40	9,290		2,163,500

1. 
   the mean is ^{∑ fx} = ^9,310 = 232.25 = 233 books
   

∑ f40

				2		(		∑ fx		)		2						(	9, 290					)	2
(ii)the standard deviation is		∑ fx			–								=		2,163,500		–									= 12.14 = 12 books
																			(40		)
	∑ f					(∑ f )					2					40							2

4. 
   Mean is the arithmetic average
   

Mode is the most frequently occurring data value Median is the middle data value

Q7 (a)	The value of fixed costs is £2,000,000
(b)
		X	0	5	10	15	20	25	30	35
		C	2,000	2,200	2,400	2,600	2,800	3,000	3,200	3,400
		R	0	938	1,750	2,438	3,000	3,438	3,750	3,938

Break even chart for paint production

£’000

4,500
4,000
																						R = 200x – 2.5x^2
3,500
3,000
																						C = 2000 + 40x
2,500
2,000
1,500
1,000
500
0
0			5					10					15				20				25				30					35
														Quantity ('000 litres)

3. 
   Break even level of production is 17,000 litres (i.e. where x = 17 – the point where revenue equals cost)