Unit 7 Averages and range 9 A company has an office building with 32 rooms. This table shows the number of people working in each room. Number of people 1 2 3 4 5 a b c d e Frequency 7 10 8 6 1 Q9a hint Copy the table. Draw an extra column for the number of people × frequency. The total of your new column gives the number of people in the building. How many people work in the building in total? What is the total frequency? Work out the mean number of people per room. Work out the range. The data could be written in a list like this: Q9c hint Range = largest number of people in a room – smallest number of people in a room. 1111111 2222222222 33333333 444444 7 1s 10 2 s 8 3s 6 4s 5 1 5 i How many values are there in the list? n+1 to find the position of the middle one. ii Use _____ 2 iii What is the median value? 10 This table shows the results for two competitors in a javelin competition. 1st throw 2nd throw 3rd throw 4th throw Liz 28.45 m 29.20 m 27.38 m 28.35 m Katie 30.24 m 29.76 m 29.84 m 20.47 m a b c d e f Work out the mean distance thrown by Liz and by Katie. Work out the median distance for Liz and for Katie. Which value affected Katie’s mean distance? Why did it not affect Katie’s median distance thrown? Which average best represents their performances? Who do you think is the better javelin thrower? Q10c hint Is there any data value that stands out as being very high or very low? Q10d hint Which type of average is not affected by an outlier? 11 This stem and leaf diagram shows weights of fish caught in a competition. 0 1 2 3 4 Find 3 1 4 2 0 4 2 6 3 2 5 2 6 5 4 8 5 Q11a hint Which number appears most in the diagram? 8 9 a the mode 8 9 Key 0|3 means 0.3 kg b the range c the median. Q11c hint Count the number of values. The position of the median is ( + 1) ÷ 2 = . 201