The frequency distribution below is a summary of the number of motorists caught speeding along the N3 during the recent festive season.

speed ( km per hour)	number of motorists
120<140	7
140<160	9
160<180	10
180<200	15
200<220	12
220<240	5
240<260	2

Question 6 (4 Marks) The table of analysis below was prepared for the purpose of calculating the measures of central tendency and variation of the grouped data.

Speed ( km per hour)	Midpoint,m	number of motorists,f	fm	fm2	cumulative frequency
120<140	130	7	910	118300	7
140<160	150	9	1350	202500	16
160<180	170	10	?	?	26
180<200	190	15	?	?	41
200<220	210	12	?	?	53
220<240	230	5	1150	264500	58
240<260	250	2	500	125000	60
		60	fm	fm2

By first calculating the missing values, determine fm and fm2 .

a) fm = 10 980 and fm2 = 2 270 000

b) fm = 12 980 and fm2 = 2 070 000

c) fm = 12 980 and fm2 = 2 270 000

d) fm = 10 980 and fm2 = 2 070 000

Question 7 (4 Marks) Determine the mean speed of the 60 motorists caught speeding.

a) 216 km per hour

b) 153 km per hour

c) 183 km per hour

d) 168 km per hour

Question 8 (4 Marks) Determine the median speed of the 60 motorists caught speeding.

a) 173.7 km per hour

b) 186.7 km per hour

c) 185.3 km per hour

d) 165.3 km per hour

Question 9 (4 Marks) Determine the mode speed of the 60 motorists caught speeding.

a) 192.5 km per hour

b) 188.5 km per hour

c) 181.6 km per hour

d) 180.8 km per hour

Question 10 (4 Marks) Determine the standard deviation and the coefficient of variation of the data.

a) The standard deviation = 28.2 km per hour and the coefficient of variation = 15.4 km per hour.

b) The standard deviation = 32.1 km per hour and the coefficient of variation = 17.5 km per hour.

c) The standard deviation = 28.2 km per hour and the coefficient of variation = 17.5 km per hour.

d) The standard deviation = 32.1 km per hour and the coefficient of variation = 15.4 km per hour