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1. Describe a situation where each of the following is the most appropriate measure of central tendency to use:. Mode. ( i ). Mode: When examining categorical data such as most popular TV show. Median. (ii).

christopherwalker
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  1. 1. Describe a situation where each of the following is the most appropriate measure of central tendency to use: Mode (i) Mode: When examining categorical data such as most popular TV show. Median (ii) Median: When examining data with outliers such as the ages of people in a swimming pool on a given day. Mean (iii) Mean: When comparing data with no outliers such as the prices of a litre of milk in different shops.

  2. 2. The following are the times (in minutes) it took 10 people to travel to work on a certain day: 13, 58, 3, 8, 8, 68, 53, 38, 4, 12 Find the mode, median and mean. (i) Mode: 8 (occurs twice) Median: Order data 3, 4, 8, 8, 12 , 13 , 38, 53, 58, 68 The median lies between the 5th and 6th position

  3. 2. The following are the times (in minutes) it took 10 people to travel to work on a certain day: 13, 58, 3, 8, 8, 68, 53, 38, 4, 12 Find the mode, median and mean. (i) Mean Mean = 26·5

  4. 2. The following are the times (in minutes) it took 10 people to travel to work on a certain day: 13, 58, 3, 8, 8, 68, 53, 38, 4, 12 Comment on your results. (ii) There is a large variation between the different measures of central tendency. Therefore, there is little information to be gleaned from these calculations. This may be due to the very small sample size. This may be as a result of people living different distances from work and using different modes of transport.

  5. 2. The following are the times (in minutes) it took 10 people to travel to work on a certain day: 13, 58, 3, 8, 8, 68, 53, 38, 4, 12 Why might some of the results to part (i) be higher or lower than each other? (iii) The data is very spread out and the values increase dramatically after the median which causes the mean to increase. The mode is based on two pieces of data only so isn’t very reliable.

  6. 3. Which measure of central tendency would be most appropriate to use for each of the following data sets? Explain your answers. 96, 98, 98, 105, 36, 87, 95, 93 (i) Median: There is an outlier (36) which would affect mean. A, B, B, B, C, A, B, B, A, B, C, B, B, B, A (ii) Mode: This is categorical data which excludes median and mean. 71, 69, 65, 73, 64, 66, 68 (iii) Mean: There are no outliers and it is numerical data.

  7. 3. Which measure of central tendency would be most appropriate to use for each of the following data sets? Explain your answers. 2, 3, 4, 4, 5, 26, 1, 28, 7 (iv) Median: The data has outliers. Blue, green, red, red, blue, yellow, black, red, white, red, green (v) Mode: The data is categorical.

  8. 4. The scores shown below were received by four quiz teams named A, B, C, and D in a table quiz. Each team reported an ‘average’ of 90. A: 80, 85, 90, 95, 100 B: 93, 92, 90, 90, 91 C: 80, 86, 95, 92, 90 D: 85, 90, 90, 90, 90 Which measure of central tendency was used by each team? A: 80, 85, 90, 95, 100 Mode: There is no mode as all values are present only once. Median: The values are already listed in ascending order. The middle number is 90. So, the median is 90. Mean: The team could have reported either the median or the mean.

  9. 4. The scores shown below were received by four quiz teams named A, B, C, and D in a table quiz. Each team reported an ‘average’ of 90. A: 80, 85, 90, 95, 100 B: 93, 92, 90, 90, 91 C: 80, 86, 95, 92, 90 D: 85, 90, 90, 90, 90 Which measure of central tendency was used by each team? B: 93, 92, 90, 90, 91 Mode: 90 (appears twice) Median: 90, 90, 91, 92, 93 Median = 91 Mean: The team reported the mode.

  10. 4. The scores shown below were received by four quiz teams named A, B, C, and D in a table quiz. Each team reported an ‘average’ of 90. A: 80, 85, 90, 95, 100 B: 93, 92, 90, 90, 91 C: 80, 86, 95, 92, 90 D: 85, 90, 90, 90, 90 Which measure of central tendency was used by each team? C: 80, 86, 95, 92, 90 Mode: There is no mode as all values are present only once. Median: 80, 86, 90, 92, 95 Median = 90 Mean: Mean: The team reported the median.

  11. 4. The scores shown below were received by four quiz teams named A, B, C, and D in a table quiz. Each team reported an ‘average’ of 90. A: 80, 85, 90, 95, 100 B: 93, 92, 90, 90, 91 C: 80, 86, 95, 92, 90 D: 85, 90, 90, 90, 90 Which measure of central tendency was used by each team? D: 85, 90, 90, 90, 90 Mode: 90 (appears 4 times) Median: The values are already listed in ascending order. The middle number is 90. So, the median is 90. Mean: The team report either the mode or the median.

  12. 5. An internet company, Flash Internet, recorded the following internet speeds (in Megabits per second) following a series of tests in an area: 1∙6, 8∙8, 2∙9, 5∙8, 3∙1, 4∙0, 6∙5, 0∙7 Find the mode, median and mean (i) Mode: None since all values appear only once Median: 0·7, 1·6, 2·9, 3·1 , 4·0 , 5·8, 6·5, 8·8 between 4th and 5th between 4th and 5th Median: 3·55

  13. 5. An internet company, Flash Internet, recorded the following internet speeds (in Megabits per second) following a series of tests in an area: 1∙6, 8∙8, 2∙9, 5∙8, 3∙1, 4∙0, 6∙5, 0∙7 Find the mode, median and mean (i) Mean: = 4·175 Mean: 4·175

  14. 5. An internet company, Flash Internet, recorded the following internet speeds (in Megabits per second) following a series of tests in an area: 1∙6, 8∙8, 2∙9, 5∙8, 3∙1, 4∙0, 6∙5, 0∙7 Comment on your results. (ii) There is no repeated data hence no mode. The data is skewed to the positive. Therefore, the mean is higher than the median. The data is quite regularly spaced which is why there isn’t a large variation between median and mean.

  15. 5. An internet company, Flash Internet, recorded the following internet speeds (in Megabits per second) following a series of tests in an area: 1∙6, 8∙8, 2∙9, 5∙8, 3∙1, 4∙0, 6∙5, 0∙7 Which average would you advise Flash Internet to use in their advertising? Why? (iii) I would advise Flash to advertise the mean speed of 4·175 as it is higher than the median of 3·55.

  16. 6. The table shows the results of a group of students in a maths test. Using your knowledge of averages, compare the male and female results. Mode: Males 41 (appears twice) Females None (all values appear once) Median: Males 20, 40, 41, 41 , 52, 66, 69 41 Females 21, 27, 51, 56 , 86, 89, 93 56

  17. 6. The table shows the results of a group of students in a maths test. Using your knowledge of averages, compare the male and female results. Mean: Males = 47 Females = 60·42 = 60·4

  18. 6. The table shows the results of a group of students in a maths test. Using your knowledge of averages, compare the male and female results. Both the median and mean show the average female result was higher than the average male result.

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