Chapter 2: Measures of central tendency
EXERCISE 2C 1 For 10 values denoted x, it is given that x = 7.4. Find: a Σx
b Σ( x + 2)
c
Σ( x − 1)
2 Twenty-five values of z are such that Σ( z − 7) = 275. Find z.
E
3 Given q = 22 and Σ( q − 4) = 3672, find the number values of q.
4 The lengths of 2500 bolts, x mm, are summarised by Σ( x − 40) = 875. Find the mean length of the bolts.
5 Six data values are coded by subtracting 13 from each. Five of the coded values are 9.3, 5.4, 3.9, 7.6 and 2.2, and the mean of the six data values is 17.6.
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P
Find the sixth coded value.
6 The SD card slots on digital cameras are designed to accommodate a card of up to 24 mm in width. Due to low sales figures, a manufacturer suspects that the machine used to cut the cards needs to be recalibrated. The widths, w mm, of 400 of these cards were measured and are coded in the following table, where x = w – 24. w – 24 (mm) No. cards ( f )
–0.15 < x < –0.1
–0.1 < x < 0
0 < x < 0.1
0.1 < x < 0.2
32
360
6
2
SA M
a Suggest a reason why the widths have been coded in this way.
b What percentage of the SD cards are too wide to fit into the slots? c Use the coded data to estimate the mean width of these 400 cards.
7 Sixteen bank accounts have been accidentally under-credited by the following amounts, denoted by $x. 917.95
917.98
918.03
917.97
918.01
917.94
918.05
918.07
918.02
917.93
918.01
917.88
918.10
917.85
918.11
917.94
To calculate x manually, Fidel and Ramon code these figures using ( x – 917) and ( x – 920), respectively. Who has the simpler maths to do? Explain your answer.
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8 Throughout her career, an athlete has been timed in 120 of her 400-metre races. Her times, denoted by t seconds, were recorded on indoor tracks 45 times and are summarised by Σ(t − 60) = 83.7, and on outdoor tracks where Σ(t − 65) = −38.7. Calculate her average 400-metre running time and comment on the accuracy of your answer. 9 All the interior angles of n triangular metal plates, denoted by y°, are measured. a State the number of angles measured and write down the value of y. b Hence, or otherwise, find the value of Σ( y − 30). 10 A data set of 20 values is denoted by x where Σ( x − 1) = 58. Another data set of 30 values is denoted by y where Σ( y − 2) = 36. Find the mean of the 50 values of x and y. Original material © Cambridge University Press 2018
FAST FORWARD You will study the mean of linear combinations of random variables in Probability and Statistics 2.
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