Unit 7 Averages and range Key point 10 The population may be divided into groups, e.g. men and women. A stratified sample contains members of each group in proportion to the size of the group. 11 There are 30 women and 20 men in a dance class. a What fraction of the dancers are women? b A stratified sample of 15 dancers is selected. How many women should there be in the sample? 12 There are 1200 students in a school. There are 200 students in Year 11. A stratified sample of 300 students is taken. How many Year 11 students should there be in the sample? Q11a hint Write the proportion as a fraction. Q11b hint Find the same fraction of 15. Q12 hint Use the same method as in Q11. 7 Knowledge check ◉◉ To work out the mean of some values: ○○ add the values together ○○ divide your answer by the number of values. Mastery lesson 7.1 ∑ f × x ◉◉ To calculate the mean from a frequency table, use mean = _______ ∑ x where fis the frequency, x is the variable and ∑means ‘the sum of’. Mastery lesson 7.1 ◉◉ To compare two sets of data, compare an average (mean, mode or median) and the range. ◉◉ The median is the middle value when the data is written in order. n+1 The median is in the _____ th position. 2 ◉◉ An outlier is an extreme value that doesn’t fit the overall pattern. Mastery lesson 7.1 Mastery lesson 7.2 Mastery lesson 7.2 ◉◉ Estimate the range of grouped data using maximum possible value – minimum possible value. Mastery lesson 7.2 ◉◉ The modal class is the class with the highest frequency. Mastery lesson 7.3 ◉◉ When the data is grouped, you can calculate an estimate for the mean using the midpoints of the classes as estimates for data values. Mastery lesson 7.4 ◉◉ In a survey, a sample is taken to represent the population. The sample must be chosen carefully to avoid bias. Mastery lesson 7.5 ◉◉ When considering sample size, you need to balance the need for accuracy with the costs and time involved in taking a large sample. Mastery lesson 7.5 ◉◉ In a random sample, every member of the population has an equal chance of being included. Mastery lesson 7.5 Reflect Look back at this unit. Which lesson made you think the hardest? Write a sentence to explain why. Begin your sentence with: Lesson ____ made me think the hardest because ____ 205