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Interpret Grouped Frequency TablesInterpret Grouped Frequency Tables
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Question 1 of 6
1. Question
A bus depot conducted a survey on how many passengers were on each bus through an 8 hour period. How many buses had less than 20 passengers?Class Class Centre (c.c.) Frequency (f) f⋅c.c. 0-4 2 5 10 5-9 7 9 63 10-14 12 13 156 15-19 17 10 170 20-24 22 7 154 25-29 27 2 54 - (37) buses
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A grouped frequency distribution table is used for larger data sets and uses classes with intervals to group the scores.First, identify which classes has less than 20 passengers.Class Class Centre (c.c.) Frequency (f) f⋅c.c. 0-4 2 5 10 5-9 7 9 63 10-14 12 13 156 15-19 17 10 170 20-24 22 7 154 25-29 27 2 54 Finally, add up the frequencies of the highlighted classes to get the total number of buses.Class Class Centre (c.c.) Frequency (f) f⋅c.c. 0-4 2 5 10 5-9 7 9 63 10-14 12 13 156 15-19 17 10 170 20-24 22 7 154 25-29 27 2 54 Total Buses = 5+9+13+10 = 37 37 buses had less than 20 passengers -
Question 2 of 6
2. Question
A bus depot conducted a survey on how many passengers were on each bus through an 8 hour period. Find the modal class.Class Class Centre (c.c.) Frequency (f) f⋅c.c. 0-4 2 5 10 5-9 7 9 63 10-14 12 13 156 15-19 17 10 170 20-24 22 7 154 25-29 27 2 54 - Modal Class = (10)- (14)
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A modal class is the group of scores with the highest frequency.Notice that the highest value in the Frequency column is 13 and it corresponds to 10-14.Class Class Centre (c.c.) Frequency (f) f⋅c.c. 0-4 2 5 10 5-9 7 9 63 10-14 12 13 156 15-19 17 10 170 20-24 22 7 154 25-29 27 2 54 In other words, the class 10-14 occurs the most frequently, and is therefore the modal class.Modal Class=10-14 -
Question 3 of 6
3. Question
A bus depot conducted a survey on how many passengers were on each bus through an 8 hour period. Find the mean.
Class Class Centre (c.c.) Frequency (f) f⋅c.c. 0-4 2 5 10 5-9 7 9 63 10-14 12 13 156 15-19 17 10 170 20-24 22 7 154 25-29 27 2 54 Round off your answer to one decimal place.- Mean = (13.2)
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Mean Formula
Mean=∑f⋅c.c.∑fRemember
A grouped frequency distribution table is used for larger data sets and uses classes with intervals to group the scores.First, find the sum of both the Frequency and f⋅c.c. columns.∑f = 5+9+13+10+7+2 = 46 ∑f⋅x = 10+63+156+170+154+54 = 607 Class Class Centre (c.c.) Frequency (f) f⋅c.c 0-4 2 5 10 5-9 7 9 63 10-14 12 13 156 15-19 17 10 170 20-24 22 7 154 25-29 27 2 54 Total =46 Total =607 Finally, use the formula to compute for the mean.Mean = ∑f⋅c.c.∑f Mean Formula Mean = 60746 Substitute values Mean = 13.2 Rounded to one decimal place Mean=13.2 -
Question 4 of 6
4. Question
The mass of 32 students was measured and the results are shown. Complete the grouped frequency distribution table and find the mean.Class Class Centre (c.c.) Frequency (f) f⋅c.c. 51-55 53 1 56-60 58 4 61-65 63 8 66-70 68 10 71-75 73 6 76-80 78 2 81-85 83 1 Total =32 Round off your answer to one decimal place.- Mean = (67.1)
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Mean Formula
Mean=∑f⋅c.c.∑fRemember
A grouped frequency distribution table is used for larger data sets and uses classes with intervals to group the scores.First, to complete the table, fill in the f⋅c.c column by multiplying f and c.c. on each row.Class Class Centre (c.c.) Frequency (f) f⋅c.c 51-55 53 1 53 56-60 58 4 232 61-65 63 8 504 66-70 68 10 680 71-75 73 6 438 76-80 78 2 156 81-85 83 1 83 Total =32 Next, find the sum of f⋅c.c. column.∑f⋅x = 53+232+504+680+438+156+83 = 2146 Class Class Centre (c.c.) Frequency (f) f⋅c.c 51-55 53 1 53 56-60 58 4 232 61-65 63 8 504 66-70 68 10 680 71-75 73 6 438 76-80 78 2 156 81-85 83 1 83 Total =32 Total =2146 Finally, use the formula to compute for the mean.Mean = ∑f⋅c.c.∑f Mean Formula Mean = 214632 Substitute values Mean = 67.1 Rounded to one decimal place Mean=67.1 -
Question 5 of 6
5. Question
A bus depot conducted a survey on how many passengers were on each bus through an 8 hour period. Find the median class.Class Class Centre (c.c.) Frequency (f) 0-4 2 5 5-9 7 9 10-14 12 13 15-19 17 10 20-24 22 7 25-29 27 2 Total =46 - Median Class = (10)- (14)
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The class where a data set’s median is located is called the median class.Add a Cumulative Frequency column to the table.To find the median, fill in the Cumulative Frequency column by adding the frequency, as seen below.Class Class Centre (c.c.) Frequency (f) Cumulative Frequency 0-4 2 5 5 5-9 7 9 5+9=14 10-14 12 13 14+13=27 15-19 17 10 27+10=37 20-24 22 7 37+7=44 25-29 27 2 44+2=46 Total =46 To check, the last entry in the Cumulative Frequency column must be equal to the
Total Frequency.Since the total number of scores is 46, the middle score should be the average of the 23rd and 24th scores.Find the row that includes the 23rd and 24th scores.Class Class Centre (c.c.) Frequency (f) Cumulative Frequency 0-4 2 5 5 5-9 7 9 5+9=14 10-14 12 13 14+13=27 15-19 17 10 27+10=37 20-24 22 7 37+7=44 25-29 27 2 44+2=46 Total =46 The third row covers all scores between the 15th and 27th position — this includes the 23rd and 24th.Since we are looking for the median class, it will be the class where the two scores are located, which is 10-14.Median Class=10-14 -
Question 6 of 6
6. Question
The mass of 32 students was measured and the results are shown. Find the median class.Class Class Centre (c.c.) Frequency (f) 51-55 53 1 56-60 58 4 61-65 63 8 66-70 68 10 71-75 73 6 76-80 78 2 81-85 83 1 Total =32 - Median Class = (66)- (70)
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The class where a data set’s median is located is called the median class.First, add a Cumulative Frequency column to the table.To find the median, fill in the Cumulative Frequency column by adding the frequency, as seen below.Class Class Centre (c.c.) Frequency (f) Cumulative Frequency 51-55 53 1 1 56-60 58 4 1+4=5 61-65 63 8 5+8=13 66-70 68 10 13+10=23 71-75 73 6 23+6=29 76-80 78 2 29+2=31 81-85 83 1 31+1=32 Total =32 To check, the last entry in the Cumulative Frequency column must be equal to the
Total Frequency.Since the total number of scores is 32, the middle score should be the average of the 16th and 17th scores.Find the row that includes the 16rd and 17th scores.Class Class Centre (c.c.) Frequency (f) Cumulative Frequency 51-55 53 1 1 56-60 58 4 1+4=5 61-65 63 8 5+8=13 66-70 68 10 13+10=23 71-75 73 6 23+6=29 76-80 78 2 29+2=31 81-85 83 1 31+1=32 Total =32 The fourth row covers all scores between the 14th and 23rd position — this includes the 16th and 17th.Since we are looking for the median class, it will be the class where the two scores are located, which is 66-70.Median Class=66-70
Quizzes
- Find Mean, Mode, Median and Range 1
- Find Mean, Mode, Median and Range 2
- Find Mean, Mode, Median and Range 3
- Create Frequency Tables & Graphs
- Interpret Frequency Tables 1
- Interpret Frequency Tables 2
- Create and Interpret Bar & Line Graphs (Histograms)
- Interpret Cumulative Frequency Tables and Charts 1
- Interpret Cumulative Frequency Tables and Charts 2
- Create Grouped Frequency Tables and Graphs
- Interpret Grouped Frequency Tables
- Create and Interpret Dot Plots (Line Plots) 1
- Create and Interpret Dot Plots (Line Plots) 2
- Finding the Interquartile Range 1
- Finding the Interquartile Range 2
- Create and Interpret Box & Whisker Plots 1
- Create and Interpret Box & Whisker Plots 2
- Create and Interpret Box & Whisker Plots 3
- Create and Interpret Box & Whisker Plots 4
- Create and Interpret Stem & Leaf Plots 1
- Create and Interpret Stem & Leaf Plots 2
- Create and Interpret Stem & Leaf Plots 3
- Create and Interpret Stem & Leaf Plots 4