(ii) For the next 50 days she leaves home at 0700 and work at 1600. She notes the time 6 spent stationary each day. This time the mean number of minutes spent stationary is 0.9. minutes and the standard deviation is Comment on these figures in comparison to the model. Extension 100 1 Aswin collected pebbles from a beach and weighed them. For these masses, m grams, he calculated the following values. . (i) Calculate the mean and variance of these masses. 260 (ii) Aswin decided that the one with the greatest mass, grams, was not typical and so decided to remove this pebble from his collection. Find the mean and variance of the 99 remaining pebbles. 10. 2 This is the histogram from question Sketch a histogram with the same mean but a larger standard deviation. 3. When drawing graphs for the data in your large data set, software will sometimes give a graph that does not display the data well. Choose a suitable graph for an aspect of the data and write instructions for how to choose options that will show the data clearly. Your instructions should be clear enough for someone else to follow. Worked solutions 1 (i) Mean , standard deviation BC (ii) and so there are no outliers. 35th 36th 2 Location of the median so it lies between the and value. 10 Median km 52nd 53rd Location of the UQ so it lies between the and value. 16 UQ km 17th 18th Location of the LQ so it lies between the and value. 4 LQ km 3 (i) Whether or not the value is included depends on the purpose for which the average and spread are being calculated; if the purpose is to get an idea of how long the project would take for a typical student, the value should be excluded as the student does not seem to be typical. Outliers like this one could have come from a false statement from the student or it might be because they have been very slow. (ii) 10 10 20 30 40 50 60 70 80 90 Time (to the nearest minutes) Frequency 5 8 8 5 3 1 0 0 1 Cumulative frequency 5 13 21 26 29 30 30 30
(ii) For the next 50 days she leaves home at 0700 and work at 1600. She notes the time spent stationary each day. This time the mean number of minutes spent stationary is 6 minutes and the standard deviation is 0.9. Comment on these figures in comparison to the model. Extension 1 Aswin collected 100 pebbles from a beach and weighed them. For these masses, m grams, he calculated the following values. . (i) Calculate the mean and variance of these masses. (ii) Aswin decided that the one with the greatest mass, 260 grams, was not typical and so decided to remove this pebble from his collection. Find the mean and variance of the remaining 99 pebbles. 2 This is the histogram from question 10. Sketch a histogram with the same mean but a larger standard deviation. 3. When drawing graphs for the data in your large data set, software will sometimes give a graph that does not display the data well. Choose a suitable graph for an aspect of the data and write instructions for how to choose options that will show the data clearly. Your instructions should be clear enough for someone else to follow. Worked solutions 1 (i) Mean , standard deviation BC (ii) and so there are no outliers. 2 Location of the median so it lies between the 35th and 36th value. Median 10 km Location of the UQ so it lies between the 52nd and 53rd value. UQ 16 km Location of the LQ so it lies between the 17th and 18th value. LQ 4 km 3 (i) Whether or not the value is included depends on the purpose for which the average and spread are being calculated; if the purpose is to get an idea of how long the project would take for a typical student, the value should be excluded as the student does not seem to be typical. Outliers like this one could have come from a false statement from the student or it might be because they have been very slow. (ii) Time (to the nearest 10 minutes) 10 20 30 40 50 60 70 80 90 Frequency 5 8 8 5 3 1 0 0 1 Cumulative frequency 5 13 21 26 29 30 30 30
429923-section-check-in-2.02-data-presentation-and-interpretation.docx