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Frequency Tables Analysis: Modal, Median, and Mean Estimation

An analysis of grouped frequency tables to estimate the modal interval, median interval, and mean to one decimal place.

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Frequency Tables Analysis: Modal, Median, and Mean Estimation

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  1. 1. Estimate the (a) modal interval, (b) median interval and (c) mean to one decimal place for each of the following grouped frequency tables: (i) (a) Modal interval: 60–70 (Highest frequency of 14) (b) Median interval : Total frequency = 10 + 8 + 12 + 14 + 6 = 50 = n The median is between the 25th and 26th position First 10 positions are in the 30–40 interval Next 8 positions are in the 40–50 interval

  2. 1. Estimate the (a) modal interval, (b) median interval and (c) mean to one decimal place for each of the following grouped frequency tables: (i) (b) Median interval : Next 12 positions are in the 50–60 interval Both 25th and 26th position are in this interval Median interval = 50–60

  3. 1. Estimate the (a) modal interval, (b) median interval and (c) mean to one decimal place for each of the following grouped frequency tables: (i) (c) Mean: Step 1: Find mid-interval values

  4. 1. Estimate the (a) modal interval, (b) median interval and (c) mean to one decimal place for each of the following grouped frequency tables: (i) (c) Mean: Step 2: Calculate mean = 54·6

  5. 1. Estimate the (a) modal interval, (b) median interval and (c) mean to one decimal place for each of the following grouped frequency tables: (ii) (a) Modal interval: 100 – 120 (Highest frequency of 6) (b) Median interval: Total frequency = 5 + 3 + 1 + 4 + 6 = 19 The median lies in the 10th position First five are in 20–40 Next three are in 40–60

  6. 1. Estimate the (a) modal interval, (b) median interval and (c) mean to one decimal place for each of the following grouped frequency tables: (ii) (b) Median interval : Next one is in 60–80 Next four are in 80–100 (contains 10th position) Median interval = 80 – 100

  7. 1. Estimate the (a) modal interval, (b) median interval and (c) mean to one decimal place for each of the following grouped frequency tables: (ii) (c) Mean: Step 1: Calculate mid-interval values.

  8. 1. Estimate the (a) modal interval, (b) median interval and (c) mean to one decimal place for each of the following grouped frequency tables: (ii) (c) Mean: Step 2: Calculate mean = 73·2

  9. 1. Estimate the (a) modal interval, (b) median interval and (c) mean to one decimal place for each of the following grouped frequency tables: (iii) (a) Modal interval: 80 – 90 (highest frequency of 32) (b) Median interval: Total frequency: 17 + 18 + 32 + 24 + 16 = 107 The median is in the 54th position First 17 are in the interval 60 – 70 Next 18 are in the interval 70 – 80

  10. 1. Estimate the (a) modal interval, (b) median interval and (c) mean to one decimal place for each of the following grouped frequency tables: (iii) (b) Median interval: Next 32 are in the interval 80 – 90 (Includes the 54th position) Median interval = 80 – 90

  11. 1. Estimate the (a) modal interval, (b) median interval and (c) mean to one decimal place for each of the following grouped frequency tables: (iii) (c) Mean: Step 1: Find mid-interval values

  12. 1. Estimate the (a) modal interval, (b) median interval and (c) mean to one decimal place for each of the following grouped frequency tables: (iii) (c) Mean: Step 2: Calculate the mean 85·4 = 85·37

  13. 1. Estimate the (a) modal interval, (b) median interval and (c) mean to one decimal place for each of the following grouped frequency tables: (iv) (a) Modal interval: 15–20 (highest frequency of 22) (b) Median interval: Total frequency = 9 + 15 + 22 + 11 + 7 = 64 = n The median lies between 32nd and 33rd position First 9 are in the interval 5–10 Next 15 are in the interval 10–15

  14. 1. Estimate the (a) modal interval, (b) median interval and (c) mean to one decimal place for each of the following grouped frequency tables: (iv) (b) Median interval: Next 22 are in the interval 15–20 (Includes 32nd and 33rd position) Median interval = 15–20

  15. 1. Estimate the (a) modal interval, (b) median interval and (c) mean to one decimal place for each of the following grouped frequency tables: (iv) (c) Mean: Step 1: Find mid-interval values

  16. 1. Estimate the (a) modal interval, (b) median interval and (c) mean to one decimal place for each of the following grouped frequency tables: (iv) (c) Mean: Step 2: Calculate mean = 16·9 (Correct to one decimal place)

  17. 2. A survey is conducted to examine the amount of money the average customer spends at a supermarket checkout. This was done with a sample of 87 people. The information was then grouped into the following intervals. Find the (i) modal interval, (ii) median interval and (iii) estimated mean amount of money spent. Modal interval: 70–100 (highest frequency of 29) (i)

  18. 2. A survey is conducted to examine the amount of money the average customer spends at a supermarket checkout. This was done with a sample of 87 people. The information was then grouped into the following intervals. Find the (i) modal interval, (ii) median interval and (iii) estimated mean amount of money spent. Median interval: (ii) Total frequency = 10 + 13+ 12+ 29 + 23 = 87 = n The median is in the 44th position First 10 are in the interval 5–25 Next 13 are in the interval 25–40

  19. 2. A survey is conducted to examine the amount of money the average customer spends at a supermarket checkout. This was done with a sample of 87 people. The information was then grouped into the following intervals. Find the (i) modal interval, (ii) median interval and (iii) estimated mean amount of money spent. Median interval: (ii) Next 12 are in the interval 40–70 Next 29 are in the interval 70–100 (Includes the 44th position) Median interval = 70–100

  20. 2. A survey is conducted to examine the amount of money the average customer spends at a supermarket checkout. This was done with a sample of 87 people. The information was then grouped into the following intervals. Find the (i) modal interval, (ii) median interval and (iii) estimated mean amount of money spent. Mean: (iii) Step 1: Find mid-interval values

  21. 2. A survey is conducted to examine the amount of money the average customer spends at a supermarket checkout. This was done with a sample of 87 people. The information was then grouped into the following intervals. Find the (i) modal interval, (ii) median interval and (iii) estimated mean amount of money spent. Mean: (iii) Step 2: Calculate the mean = 75·546 = €75·55

  22. 3. The weights of 100 objects (in kg) were measured. The results are shown in the table below. Draw a histogram of the results shown in the table. (i)

  23. 3. The weights of 100 objects (in kg) were measured. The results are shown in the table below. What is the modal interval? (ii) Modal interval = 15–20 kg

  24. 3. The weights of 100 objects (in kg) were measured. The results are shown in the table below. Estimate the mean weight of the objects. (iii) Step 1: Find mid- interval values

  25. 3. The weights of 100 objects (in kg) were measured. The results are shown in the table below. Estimate the mean weight of the objects. (iii) Step 2: Calculate mean = 16·14 16·1 kg (correct to one decimal)

  26. 3. The weights of 100 objects (in kg) were measured. The results are shown in the table below. If the mean for a further 100 objects is 18∙5, estimate the mean for the 200 objects. (iv) mean for next 100 objects = 18·5 mean for first 100 objects = 16·1 Mean for the 200 objects = 17∙3 kg

  27. 4. The ages of 20 musicians are listed below. 6, 11, 14, 17, 7, 20, 19, 15, 26, 21, 13, 15, 19, 19, 29, 11, 18, 13, 8, 14 Calculate the mean to one decimal place from the list. (i)

  28. 4. The ages of 20 musicians are listed below. 6, 11, 14, 17, 7, 20, 19, 15, 26, 21, 13, 15, 19, 19, 29, 11, 18, 13, 8, 14 Group the data into intervals: 6–10, 11–15, 16–20 etc., and then estimate the mean to one decimal place from the grouped data. (ii) Step 1: Find the mid–interval values

  29. 4. The ages of 20 musicians are listed below. 6, 11, 14, 17, 7, 20, 19, 15, 26, 21, 13, 15, 19, 19, 29, 11, 18, 13, 8, 14 Group the data into intervals: 6–10, 11–15, 16–20 etc., and then estimate the mean to one decimal place from the grouped data. (ii) Step 2: Calculate mean = 15·8

  30. 5. David has just moved house. In the area, he has moved to there are two doctor’s surgeries. David doesn’t like to wait when he goes to the doctor so he decides to gather some data to help him decide which doctor to attend. Surgery A Surgery B Draw a histogram of the results shown in the table. (i)

  31. 5. David has just moved house. In the area, he has moved to there are two doctor’s surgeries. David doesn’t like to wait when he goes to the doctor so he decides to gather some data to help him decide which doctor to attend. Surgery A Surgery B Estimate the mean for both sets of data. (ii) Surgery A mean: Step 1: Find mid-interval values

  32. 5. David has just moved house. In the area, he has moved to there are two doctor’s surgeries. David doesn’t like to wait when he goes to the doctor so he decides to gather some data to help him decide which doctor to attend. Surgery A Surgery B Estimate the mean for both sets of data. (ii) Step 2: Calculate mean = 12·7 minutes

  33. 5. David has just moved house. In the area, he has moved to there are two doctor’s surgeries. David doesn’t like to wait when he goes to the doctor so he decides to gather some data to help him decide which doctor to attend. Surgery A Surgery B Estimate the mean for both sets of data. (ii) Surgery B mean: Step 1: Find mid-interval values

  34. 5. David has just moved house. In the area, he has moved to there are two doctor’s surgeries. David doesn’t like to wait when he goes to the doctor so he decides to gather some data to help him decide which doctor to attend. Surgery A Surgery B Estimate the mean for both sets of data. (ii) Step 2: Calculate mean = 12·3 minutes

  35. 5. David has just moved house. In the area, he has moved to there are two doctor’s surgeries. David doesn’t like to wait when he goes to the doctor so he decides to gather some data to help him decide which doctor to attend. Surgery A Surgery B Which surgery would you recommend for David to attend? Justify your answer by referring to the histograms and the estimated mean. (iii) There are several answers possible here: Surgery B. Surgery A has a slightly longer mean waiting time. Surgery A. Surgery A has only 7 people who waited 20–25 mins whereas Surgery B has 11 people.

  36. 5. David has just moved house. In the area, he has moved to there are two doctor’s surgeries. David doesn’t like to wait when he goes to the doctor so he decides to gather some data to help him decide which doctor to attend. Surgery A Surgery B Which surgery would you recommend for David to attend? Justify your answer by referring to the histograms and the estimated mean. (iii) There are several answers possible here: Surgery B. Surgery A has only 6 people who waited 0–5 mins whereas surgery B has 13. Surgery B. It has less variation in wait-times which would cause me to recommend it over Surgery A.

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