Statistics Topical question [Pearson Edexcel Mathematics B (4MB1) 2014-2016]

 Before practising Statistics topical questions, please check the list if you have already known. 

-Measures of central tendicies - Mean, medium, mode; 
-Measure of spreads - range, interqutine range, 
-Cumulative frequency, histogram, box and whisker plots, Sterm and leaf diagrams, Scatter diagrams and correlation

Are you ready? Lets go on....

1	(Edexcel/Math B/2014/jan/paper01R/q25) A school class has 30 pupils. The shoe size of each pupil is recorded and this table shows information about these results.  \[ \begin{array}{|c|c|c|c|c|c|c|c|} \hline \text{Size of shoe} & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ \hline \text{Number of pupils} & 2 & 5 & 8 & 9 & 3 & 2 & 1 \\ \hline \end{array} \] For this information, find (a)the mode [1] (b)the median [2] (c)the mean [3]
2	(Edexcel/Math B/2014/june/paper01R/q19) Here is a list of eight whole numbers: \[ 8,\ 19,\ 14,\ 15,\ 23,\ 6,\ 4,\ x \] The median of these eight numbers is 12. (a) Find the value of \(x\).[2] (b) Calculate the mean of the eight numbers. [2]
3	(Edexcel/Math B/2014/jan/paper01/q22) A pupil waits at a bus stop each day for the school bus. Here are the number of minutes waited each day for eleven days: \[ 6,\ 5,\ 11,\ 9,\ 4,\ 8,\ 5,\ 14,\ 6,\ 5,\ 4 \] (a) Write down the mode.[1] (b) Find the median. [2] (c) Workout the mean [2]
4	(Edexcel/Math B/2015/jan/paper01R/q19) Here is a list of eight integers:  (Numbers not fully given in the image, but second part states:) The value of \(x\) is three times the median of these eight integers. (a) Find the median.[2] (b) Work out the numerical value of the mean of the eight integers.[2]
5	(Edexcel/Math B/2015/june/paper01/q17) Here are ten numbers: \[ 1,\ 2,\ 2,\ 3,\ 4,\ 5,\ 5,\ 5,\ 6,\ 6,\ x \]  (a) Write down: [2] (i) mode of the ten numbers, (ii) median of the ten numbers. (b) Given also that \[ \text{mean} = 3 \times \text{mode} - \text{median}, \]  find the value of \(x\).[2]
6	(Edexcel/Math B/2016/june/paper01/q18) Here are 8 numbers: \[ 5.9,\ 6.3,\ 6.7,\ 6.9,\ 7.5,\ 8.1,\ 8.1,\ 8.9 \]  (a) Find the median of the 8 numbers.[2] (b) Calculate the mean of the 8 numbers.[2]
7	(Edexcel/Math B/2014/jan/paper01/q18) In one week, a company made four types of telephone call: selling calls, purchasing calls, financial calls and delivery calls. In the week, the company made 420 selling calls, 160 purchasing calls and 64 financial calls. A pie chart was drawn to show this information. The angle on the pie chart for selling calls was \(210^\circ\). (a) Calculate the total number of calls made that week.[2] (b) Hence calculate the number of delivery calls made in the week. [2]
8	(Edexcel/Math B/2014/jan/paper01R/q5) The income for an engineering company in one year was \(£1,800,000\). The pie chart shows information about how this money was used. (a) Calculate, in \(£\), the amount of money used for Staff salaries in the year.[2] Equipment and Running costs together used \(17.5\%\) of the income.  (b) Express the Profit as a percentage of the income for the year. Give your answer to 3 significant figures. [4]
9	(Edexcel/Math B/2014/june/paper01/q20) In the town of Electoria, four candidates stood in the election for town mayor.  The number of votes each candidate received is represented by the pie chart. The number of votes Candidate D received is 3075 and the angle of the sector for Candidate D is \(75^\circ\). (a) Calculate the total number of votes received by all four candidates. [2] Candidate A won the election. The angle of the sector for Candidate A is \(5^\circ\) greater than the angle of the sector for Candidate B. (b) Calculate how many more votes Candidate A received than Candidate B. [2]
10	(Edexcel/Math B/2015/jan/paper01/q14) Bob has a box of toy bricks. He counts the numbers of red, yellow, green, black and white bricks in the box. Here are his results: \[ \begin{array}{|c|c|} \hline \text{Colour} & \text{Number} \\ \hline \text{Red} & 350 \\ \text{Yellow} & 236 \\ \text{Green} & 154 \\ \text{Black} & 63 \\ \text{White} & 197 \\ \hline \end{array} \]  Bob is going to draw a pie chart for his results. Calculate the size, in degrees, of the angle of the sector for red bricks.[3]
	to be continued....

Answer Key for Statistics (2014-2016)

1.   (a) 6 (b) 5.5  (c)  5.53
2.   (a) 10 (b) $12.4 \quad $
3.   (a) 5 (b) 6 (c) 7
4.   (a) $14 \quad$ (b) $16.5 \quad$
5.   (a)(i) 5 (ii) 4.5 (b) $72 \quad $
6.   (a) $ 7.2 $ (b) $ 7.3$ 
7.   (a) 720 calls (b) 76 deli calls
8.   (a) $£ 1160000$ (b) $5.83 \%$
9.   (a) $14760 \quad$ (b) 205
10.   $126^{\circ} \quad$
11.   $93^\circ \quad$
12.   (a) 2 (b) $4 $ (c) $\frac{71}{20}$ 
13.   (a) 12,45,50,40 (b) $ 20 \% \quad$
14.   (a) $ 40,60 $ (b) $ 0.5,7 $
15.   $22,48,20$
16.   $70,6$ , histogrom
17.   $12,14,5,1 \quad$
18.   (a) $58$ minutes (b) Heights $\frac{1}{3}, 1.4,4.5,2.7$ and 3.2 (c) $\frac{96}{200}$
19.   (a) $20,6,16 \quad$ (b) $\frac{44}{60} \quad $
20.   (a) histogram (b) 43 years
21.   (a) 5.52 (b) 6,3,2
22.   (a) $46.2 \mathrm{~km} / \mathrm{hr}$ (b) $\frac{37}{100}$ (c) histogram  (d) $\frac{x-4}{x-1}$
23.   (a) $\quad 40<L \leqslant 65$ (b) 49 (c) histogram