(a) Calculate an estimate for the mean price paid for a new computer. (b) Calculate the value by the end of the third year.

Transcription

1 Mean from grouped Freque Question 1 National curriculum reference: NA2e,3e,3j, HD4b Date: June 1999 Paper: 6 Ben asked 50 people how much they paid for a new computer. The results are shown in this frequency table. Price ( P) Number of Computers 0 < P < P < P < P < P (a) Calculate an estimate for the mean price paid for a new computer. By the end of the year, the value of a computer falls by 15 % of its value at the start of the year. A new computer has a value of (b) Calculate the value by the end of the third year. simulatedpagebreakquestion 2 National curriculum reference: HD4e Date: November 2000 Paper: 6 75 boys took part in a darts competition. Each boy threw darts until he hit the centre of the dartboard. The number of darts thrown by the boys are grouped in this frequency table.

2 Number of darts thrown Frequency 1 to to to to to to (a) Work out the class interval which contains the median. (b) Work out an estimate for the mean number of darts thrown by each boy. simulatedpagebreakquestion 3 National curriculum reference: HD4e,2d Date: June 2001 Paper: 6 The table shows the number of students in three groups attending Maths City High School last Monday. No student belonged to more than one group. Group Number of students A 135 B 225 C 200 Mrs Allen carried out a survey about the students' travelling times from home to school last Monday.

3 Mrs Allen worked out that the mean time for Group A students was 24 minutes, the mean time for Group B students was 32 minutes, the mean time for Group C students was the same as the mean time for all 560 students. (a) Work out the mean time for all 560 students.... minutes Mrs Allen interviewed some of these students. She used a stratified sample of 50 students according to each group. (b) Work out the number of students from each group which should have been in her sample of 50. Group A... Group B... Group C... (3 marks) simulatedpagebreakquestion 4 National curriculum reference: HD4e Date: November 2001 Paper: 6 Jason grows potatoes. He weighed 100 potatoes and recorded the weights to the nearest gram. The table shows information about the weights (w) of the 100 potatoes. Weight (w) grams Frequency 0 w < w < w < w < w < w < (a) Work out an estimate for the mean weight of these potatoes.

4 ... g (b) Find the class interval that contains the median. simulatedpagebreakquestion 5 National curriculum reference: HD4b,4d Date: June 1999 Paper: 3 Tony carries out a survey about the words in a book. He chooses a page at random. He then counts the number of letters in each of the first hundred words on the page. The table shows Tony's results. Number of letters in a word Frequency A word is chosen at random from the hundred words. (a) What is the probability that the word will have 5 letters? The book has words. (b) Estimate the number of 5 letter words in the book. The book has 125 pages with a total of words. The words on each of the first 75 pages are counted. The mean is 192. (c) Calculate the mean number of words per page for the remaining 50 pages. simulatedpagebreakquestion 6 National curriculum reference: HD4b Date: November 1998 Paper: 3

5 The table gives information about the ages, in years, of 100 aeroplanes. (a) Work out an estimate of the mean age of the aeroplanes. Age Frequency (t years) 0 < t < t < t < t < t 25 1 (b) Complete the cumulative frequency table. (c) On the grid, draw a cumulative frequency graph for your table. Age (t years) 0 < t 5 0 < t 10 0 < t 15 0 < t 20 0 < t 25 Frequency (1 mark) (d) Use your graph to find an estimate of the upper quartile of the ages. Show your method clearly. simulatedpagebreakquestion 7 National curriculum reference: HD4b Date: November 1998 Paper: 5

6 The table gives information about the ages, in years, of 100 aeroplanes. (a) Work out an estimate of the mean age of the aeroplanes. Age Frequency (t years) 0 < t < t < t < t < t 25 1 (b) Complete the cumulative frequency table. (c) On the grid, draw a cumulative frequency graph for your table. Age (t years) 0 < t 5 0 < t 10 0 < t 15 0 < t 20 0 < t 25 Frequency (1 mark) (d) Use your graph to find an estimate of the upper quartile of the ages. Show your method clearly. simulatedpagebreakquestion 8 National curriculum reference: HD4b Date: June 1998 Paper: 6

7 A class took a test. The mean mark of the 20 boys in the class was The mean mark of the 10 girls in the class was (a) Calculate the mean mark for the whole class. 5 pupils in another class took the test. Their marks, written in order, were 1, 2, 3, 4 and x. The mean of these 5 marks is equal to twice the median of these 5 marks. (b) Calculate the value of x. (3 marks) simulatedpagebreakquestion 9 National curriculum reference: HD4b Date: November 1997 Paper: 5 Andrew did a survey at the seaside for his science coursework. He measured the lengths of 55 pieces of seaweed. The results of the survey are shown in the table. Length of seaweed (L cm) Frequency 0 < L < L < L < L < L < L < L Andrew needs to calculate an estimate for the mean length of the pieces of seaweed. (a) Work out an estimate for the mean length of the piece of seaweed. Give your answer correct to 1 decimal place. (b) Write down the interval that contains the median length of a piece of seaweed. simulatedpagebreakquestion 10 National curriculum reference: HD4b Date: June 1997 Paper: 6

8 A survey was carried out to find how much time was needed by a group of pupils to complete homework set on a particular Monday evening. The results are shown in the table below. T i m e, t h o u r s, s p e n t o n h o m e w o r k N u m b e r o f p u p i l s < t < t < t < t 4 1 Calculate an estimate for the mean time spent on homework by the pupils in the group. simulatedpagebreakquestion 11 National curriculum reference: HD4b Date: June 1996 Paper: 5 Bronwen owns a pet shop. The table gives information about the weights of hamsters in Bronwen's shop. W e i g h t w o f N u m b e r o f h a m s t e r s i n g h a m s t e r s 2 8 < w < w < w < w 36 2 Calculate an estimate for the mean weight of the hamsters in Bronwen's shop. simulatedpagebreakquestion 12 National curriculum reference: HD4b Date: June 1998 Paper: 5 Twenty five people took part in a competition. The points scored are grouped in the frequency table below.

9 Points scored Number of people 1 to to to to to to 30 2 (a) Work out an estimate for the mean number of points scored. (b) Complete the table below to show the cumulative frequency for this data. Points scored Cumulative frequency 1 to 5 6 to to to to to 30 (c) On graph paper, draw a cumulative frequency graph for this data. (d) Use your graph to find an estimate for the median of this data. (3 marks) (3 marks) (1 mark)

10 simulatedpagebreakquestion 13 National curriculum reference: HD4e Date: June 2000 Paper: 5

11 Sybil weighed some pieces of cheese. The table gives information about her results. Weight (w) grams Frequency 90 < w < w < w < w Work out an estimate of the mean weight.... grams simulatedpagebreakquestion 14 National curriculum reference: HD4e Date: November 2000 Paper: 5 A shop employs 8 men and 2 women. The mean weekly wage of the 10 employees is 396. The mean weekly wage of the 8 men is 400. Calculate the mean weekly wage of the 2 women.... simulatedpagebreakquestion 15 National curriculum reference: HD4e,4a Date: June 2001 Paper: 6 The grouped frequency table shows information about the number of hours worked by each of 200 headteachers in one week.

12 Number of hours worked (t) Frequency 0 < t < t < t < t < t < t (a) Work out an estimate of the mean number of hours worked by the headteachers that week.... hours (b) Complete the cumulative frequency table. Number of hours worked (t) Cumulative Frequency 0 < t < t 40 0 < t 50 0 < t 60 0 < t 70 0 < t 80 (1 mark) (c) On the grid below, draw a cumulative frequency graph for your table.

13 (d) Use your graph to find an estimate for the interquartile range of the number of hours worked by the headteachers that week. Show your method clearly.... hours

14 simulatedpagebreakquestion 16 National curriculum reference: HD4e Date: January 2003 Paper: 10 Marcus collected some pebbles. He weighed each pebble. The grouped frequency table gives some information about weights. Weight (w grams) Frequency 50 w < w < w < w < w < Work out an estimate for the mean weight of the pebbles.... grams simulatedpagebreakquestion 17 National curriculum reference: HD4e Date: June 2002 Paper: 6 27 boys and 34 girls took the same test. The mean mark of the boys was 76. The mean mark of the girls was 82. Calculate the mean mark of all these students. Give your answer correct to 1 decimal place.... (3 marks)

15 simulatedpagebreakquestion 18 National curriculum reference: HD4a Date: March 2003 Paper: 10 The cumulative frequency diagram opposite gives information about the prices of 120 houses. (a) Find an estimate for the number of houses with prices less than (1 mark) (b) Work out an estimate for the interquartile range of the prices of the 120 houses....

16 simulatedpagebreakquestion 19 National curriculum reference: HD4a Date: November 2002 Paper: 6 35 students with Saturday jobs took part in a survey. They were asked the hourly rate of pay for their jobs. This information is shown in the grouped frequency table below. Hourly rate of pay ( x) Frequency 3.00 < x < x < x < x < x < x (a) Work out an estimate for the mean hourly rate of pay. Give your answer to the nearest penny. (b) (i) Complete the table below to show the cumulative frequency.... Hourly rate of pay ( x) 3.00 < x < x < x < x < x < x 6.00 Cumulative Frequency (ii) Draw the cumulative frequency on the grid below.

17 (c) Use your graph to work out an estimate for the interquartile range....