Valuation, v, of painting ( ) Frequency Frequency density. 0 v < v < v < v <

Transcription

1 Q experts value a painting. The grouped frequency distribution shows information about the valuations and the frequency density of some of the groups. Valuation, v, of painting ( ) Frequency Frequency density 0 v < v < v < v < Draw a fully labelled histogram for the data on the grid below (Total 5 marks) Page 1 of 16

2 Q2. The owner of a museum wants to know the distance that visitors travel to the museum. Information is collected from visitors. The table shows this information. Distance travelled, d (miles) Number of visitors 0 < d < d < d < d (a) Construct a histogram on the grid below to show this information. Page 2 of 16

3 (3) (b) A stratified sample of 100 is taken from these visitors. Calculate the number in the sample who travel more than five miles. Answer... (2) (Total 5 marks) Q3. The table shows the weight of the first 100 parcels posted over the counter at a Post Office. Weight, w (grams) Frequency 0 < w < w < w < w Page 3 of 16

4 (a) Draw a fully labelled histogram to show the weights of the 100 parcels. (3) Page 4 of 16

5 (b) Estimate the probability that the first two parcels posted that week were both over 500 grams in weight. Answer... (3) (Total 6 marks) Q4. The histogram shows the test scores of 320 children in a school. Page 5 of 16

6 (a) Find the median score. Answer... (2) (b) Find the interquartile range of the scores. Answer... (2) (Total 4 marks) Q5. The histogram shows information about how much time was spent in a supermarket by 100 shoppers. (a) Complete this frequency table: Time, t (minutes) 0 < t 5 5 < t < t < t < t 80 Number of shoppers (2) Page 6 of 16

7 (b) 20% of the shoppers are in the supermarket for more than T minutes. Calculate an estimate of the value of T.... Answer... (2) (Total 4 marks) Q6. Batteries are tested by putting them into toys and seeing how long they last. Here are the results of 60 tests. Time, t (minutes) Frequency 500 t < t < t < t < t < (a) Draw a histogram to show this information. (3) Page 7 of 16

8 (b) Use your histogram, or otherwise, to estimate the median life of a battery. Answer... minutes (2) (Total 5 marks) Q7. The table shows the distribution of ages in a health club. Age, y (years) Frequency 0 < y < y < y < y < y Page 8 of 16

9 (a) (i) Draw a histogram to illustrate this data (3) (ii) Members over 65 pay a reduced subscription. Estimate how many members are over Answer... (1) Page 9 of 16

10 (b) This histogram shows the pulse rates of some of the members of the club. 60 of the members have a pulse rate lower than 50 beats per minute. How many members have a pulse rate greater than 90 beats per minute? Answer... (4) (Total 8 marks) Page 10 of 16

11 Q8. The histogram represents the birth weights of 150 babies. Thirty babies weighed over 4.5 kg Babies weighing under 2 kg are taken to the Special Care Baby Unit. Calculate the number of babies taken to the Special Care Baby Unit Answer... (Total 3 marks) Page 11 of 16

12 or and 10 Method for one of the missing frequencies Their 30 Their 10 and Their answer divided by 500 (46 and 0.092) Final frequency and frequency density Bars correct widths Bars correct height_s Condone the third bar missing for these two marks. B1ft B1ft B1ft [5] M2. (a) Attempts frequency density with at least one correct Correct frequency densities 560, 1240, 377( ), 92 Histogram drawn correctly Correctly numbered scale. No need for labels or title. Tolerance small square of their scale ft (b) or 100 or 8.( ) oe 91.5(1 ) 92 [5] Page 12 of 16

13 M3. (a) f class width for at least 3 values 0.068, 0.056, 0.022, Allow scaled values Fully labelled correct histogram (b) P(first over 500) = B [6] M4. Finds total of at least first 4 bars 60, 40, 100, 40, (30, 50) Finds cumulative total at least as far as , 100, 200, (240, 270, 320). NB these can occur in either part and cumulative totals implies bar totals. Median = 102 IQR = 35 Correct answer for either part scores 2 Sc No previous Ms awarded or seen allow Ml. [4] M5. (a) or and 33 Sight of 21 or 33 indicates Page 13 of 16

14 (b) (Good) attempt at cutting off area Calculation of 16 mins ( mins) or 4 mins ( 20 mins)... T = 64 must be correct [4] M6. (a) Using frequency densities Correct frequency densities Height & widths plotted correctly At least 2 correct Look for consistent use of key 4 out of 5 correct... look for evidence on graph ± ½ square for their vertical scale B1 (b) Good attempt to halve the area 735 minutes Or halving the frequency + attempt at calculation (could be a cum. freq. calculation) [5] M7. (a) (i) fds = frequency class width for attempt to find f.d s or use of scaling method = 5, 70, 170, 50, 20 if all correct or height_s in proportion. e.g. 1, 14, 34, 10, 4 or 25, 350, 850, 250, 100 Plotting between limits to correct height_s ft their fds No scale on graph deduct a mark ft (ii) B1 Page 14 of 16

15 (b) 60 members = area below 50 This mark is for identifying that the area below 50 is equivalent to 60 members area above 90 e.g. 33 rows, 165 squares, 6.6 squares B1 scale factor = 1.5 or ratio = 90:165= 1:1.833 Fraction = 165/90 = 11/6 oe e.g. members per square, or 1.5 squares per person = = = 110 ft their scale factor if both s awarded but do not award if answer is not integer ft [8] M8. 1 sq cm = 5 babies 150 little squares = 30 or [3] Page 15 of 16

16 Page 16 of 16