Number of fillings Frequency q 4 1. (a) Find the value of q. (2)

Transcription

1 1. The table below shows the frequency distribution of the number of dental fillings for a group of 25 children. Number of fillings Frequency q 4 1 Find the value of q. Use your graphic display calculator to find (iii) the mean number of fillings; the median number of fillings; the standard deviation of the number of fillings. (4) matches were played in a football tournament. The following table shows the number of goals scored in all matches. Number of goals Number of matches Find the mean number of goals scored per match. Find the median number of goals scored per match. A local newspaper claims that the mean number of goals scored per match is two. (c) Calculate the percentage error in the local newspaper s claim.

2 3. The temperatures in C, at midday in Geneva, were measured for eight days and the results are recorded below. The mean temperature was found to be 7 C. 7, 4, 5, 4, 8, T, 14, 4 Find the value of T. Write down the mode. (1) (c) Find the median. 4. State which of the following sets of data are discrete. (iii) (iv) (v) Speeds of cars travelling along a road. Numbers of members in families. Maximum daily temperatures. Heights of people in a class measured to the nearest cm. Daily intake of protein by members of a sporting team.

3 The boxplot below shows the statistics for a set of data data values For this data set write down the value of (iii) the median; the upper quartile; the minimum value present. (c) Write down three different integers whose mean is An atlas gives the following information about the approximate population of some cities in the year The population of Nairobi has accidentally been left out. City Population in Millions Melbourne 3.2 Bangkok 7.2 Nairobi Paris 9.6 São Paulo 17.7 Tokyo 28.0 Seattle 2.1 The atlas tells us that the mean population for this group of cities is million. Calculate the population of Nairobi.

4 Which city has the median population value? (Total 8 marks) pupils in a class were asked to estimate the number of sweets in a jar. The following stem and leaf diagram gives their estimates. Stem Leaf 2, 4, 7, 8, 9 1, 1, 2, 3, 8, 9 0, 2, 2, 4, 6, 6, 7, 8, 8 0, 0, 1, 3, 4, 5, 5, 7 1, 2, 2 Key: 4 7 represents 47 sweets For the pupils estimates, write down (iii) the median; the lower quartile; the upper quartile.

5 Draw a box and whisker plot of the pupils estimates using the grid below. 7. The table shows the number of children in 50 families. Number of children Write down the value of T. Find the values of m, p and q. Frequency Cumulative frequency m p q T (Total 4 marks)

6 Mathematics students in a school sat an examination. Their scores (given as a percentage) were summarized on a cumulative frequency diagram. This diagram is given below. Complete the grouped frequency table for the students. Examination Score x (%) 0 x < x < x < x < x 100 Frequency Write down the mid-interval value of the 40 < x 60 interval. (1)

7 (c) Calculate an estimate of the mean examination score of the students. 9. The weights of 90 students in a school were recorded. The information is displayed in the following table. Weight (kg) Number of students 40 w < w < w < w < Write down the mid interval value for the interval 50 w < 60. (1) Use your graphic display calculator to find an estimate for the mean weight; the standard deviation. (c) Find the weight that is 3 standard deviations below the mean.

8 10. Five pipes labelled, 6 metres in length, were delivered to a building site. The contractor measured each pipe to check its length (in metres) and recorded the following; 5.96, 5.95, 6.02, 5.95, Find the mean of the contractor s measurements. Calculate the percentage error between the mean and the stated, approximate length of 6 metres Calculate , giving your answer correct to the nearest integer; in the form a 10 k, where 1 a < 10, k. 11. A survey was conducted of the number of bedrooms in 208 randomly chosen houses. The results are shown in the following table. Number of bedrooms Number of houses (c) State whether the data is discrete or continuous. Write down the mean number of bedrooms per house. Write down the standard deviation of the number of bedrooms per house. (1) (1) (d) Find how many houses have a number of bedrooms greater than one standard deviation above the mean.

9 12. The diagram shows the cumulative frequency graph for the time t taken to perform a certain task by 2000 men. Use the diagram to estimate (iii) the median time; the upper quartile and the lower quartile; the interquartile range. (4) Find the number of men who take more than 11 seconds to perform the task. (c) 55 % of the men took less than p seconds to perform the task. Find p.

10 The times taken for the 2000 men were grouped as shown in the table below. Time Frequency 5 t < t < t < 20 a 20 t < 25 b (d) Write down the value of a; b. (e) Use your graphic display calculator to find an estimate of the mean time; the standard deviation of the time. Everyone who performs the task in less than one standard deviation below the mean will receive a bonus. Pedro takes 9.5 seconds to perform the task. (f) Does Pedro receive the bonus? Justify your answer. (Total 17 marks) 13. Write down the following numbers in increasing order. 3.5, , 60730, , , π, (c) Write down the median of the numbers in part. State which of the numbers in part is irrational.

11 14. Complete the following table of values for the height and weight of seven students. Values Mode Median Mean Standard deviation Height (cm) 151, 158, 171, 163, 184, 148, Weight (kg) 53, 61, 58, 82, 45, 72, (4) The ages (in months) of seven students are 194, 205, 208, 210, 200, 226, 223. Represent these values in an ordered stem and leaf diagram. 15. The heights in cm of the members of 4 volleyball teams A, B, C and D were taken and represented in the frequency histograms given below. frequency A frequency B height (cm) height (cm) frequency C frequency D height (cm) height (cm)

12 The mean x and standard deviation σ of each team are shown in the following table. I II III IV x σ Match each pair of x and σ (I, II, III, or IV) to the correct team (A, B, C or D). x and σ Team I II III IV 16. The following table shows the age distribution of teachers who smoke at Laughlin High School. Ages Number of smokers 20 x < x < x < x < x < 70 3 Calculate an estimate of the mean smoking age.

13 On the following grid, construct a histogram to represent this data. (Total 4 marks)

14 17. The following stem and leaf diagram gives the heights in cm of 39 schoolchildren. Stem Leaf Key 13 2 represents 132 cm , 3, 3, 5, 8, 1, 1, 1, 4, 5, 5, 9, 3, 4, 4, 6, 6, 7, 7, 7, 8, 9, 9, 1, 2, 2, 5, 6, 6, 7, 8, 8, 4, 4, 4, 5, 6, 6, 0, State the lower quartile height. (iii) State the median height. State the upper quartile height. Draw a box and whisker plot of the data using the axis below height in cm 18. The following table shows the times, to the nearest minute, taken by 100 students to complete a mathematics task. Time (t) minutes Number of students Construct a cumulative frequency table. (Use upper class boundaries 15.5, 20.5 and so on.)

15 On graph paper, draw a cumulative frequency graph, using a scale of 2 cm to represent 5 minutes on the horizontal axis and 1 cm to represent 10 students on the vertical axis. (c) Use your graph to estimate the number of students that completed the task in less than 17.5 minutes; 3 the time it will take for of the students to complete the task. 4 (Total 7 marks)