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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?`\text(Class)` `\text(Class Centre) (c.c.)` `\text(Frequency) (f)` `f⋅c.c.` `04` `2` `5` `10` `59` `7` `9` `63` `1014` `12` `13` `156` `1519` `17` `10` `170` `2024` `22` `7` `154` `2529` `27` `2` `54`  (37) `\text(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.` 04 2 5 10 59 7 9 63 1014 12 13 156 1519 17 10 170 2024 22 7 154 2529 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.` 04 2 5 10 59 7 9 63 1014 12 13 156 1519 17 10 170 2024 22 7 154 2529 27 2 54 `\text(Total Buses)` `=` `5+9+13+10` `=` `37` `37 \text(buses had less than) 20 \text(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.`\text(Class)` `\text(Class Centre) (c.c.)` `\text(Frequency) (f)` `f⋅c.c.` `04` `2` `5` `10` `59` `7` `9` `63` `1014` `12` `13` `156` `1519` `17` `10` `170` `2024` `22` `7` `154` `2529` `27` `2` `54`  `\text(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 `1014`.Class Class Centre `(c.c.)` Frequency `(f)` `f⋅c.c.` 04 2 5 10 59 7 9 63 1014 12 13 156 1519 17 10 170 2024 22 7 154 2529 27 2 54 In other words, the class `1014` occurs the most frequently, and is therefore the modal class.`\text(Modal Class)=1014` 
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.
`\text(Class)` `\text(Class Centre) (c.c.)` `\text(Frequency) (f)` `f⋅c.c.` `04` `2` `5` `10` `59` `7` `9` `63` `1014` `12` `13` `156` `1519` `17` `10` `170` `2024` `22` `7` `154` `2529` `27` `2` `54` Round off your answer to one decimal place. `\text(Mean )=` (13.2)
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Mean Formula
$$\text{Mean}=\frac{\color{#314EC4}{\sum f⋅c.c.}}{\color{#9202AA}{\sum f}}$$Remember
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.`sum f` `=` `5+9+13+10+7+2` `=` `46` `sum f⋅x` `=` `10+63+156+170+154+54` `=` `607` Class Class Centre `(c.c.)` Frequency `(f)` `f⋅c.c` 04 2 5 10 59 7 9 63 1014 12 13 156 1519 17 10 170 2024 22 7 154 2529 27 2 54 `\text(Total) =46` `\text(Total) =607` Finally, use the formula to compute for the mean.`\text(Mean)` `=` $$\frac{\color{#314EC4}{\sum f⋅c.c.}}{\color{#9202AA}{\sum f}}$$ Mean Formula `\text(Mean)` `=` $$\frac{\color{#314EC4}{607}}{\color{#9202AA}{46}}$$ Substitute values `\text(Mean)` `=` `13.2` Rounded to one decimal place `\text(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.` 5155 53 1 5660 58 4 6165 63 8 6670 68 10 7175 73 6 7680 78 2 8185 83 1 `\text(Total) =32` Round off your answer to one decimal place. `\text(Mean )=` (67.1)
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Mean Formula
$$\text{Mean}=\frac{\color{#314EC4}{\sum f⋅c.c.}}{\color{#9202AA}{\sum f}}$$Remember
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` 5155 53 1 53 5660 58 4 232 6165 63 8 504 6670 68 10 680 7175 73 6 438 7680 78 2 156 8185 83 1 83 `\text(Total) =32` Next, find the sum of `f⋅c.c.` column.`sum f⋅x` `=` `53+232+504+680+438+156+83` `=` `2146` Class Class Centre `(c.c.)` Frequency `(f)` `f⋅c.c` 5155 53 1 53 5660 58 4 232 6165 63 8 504 6670 68 10 680 7175 73 6 438 7680 78 2 156 8185 83 1 83 `\text(Total) =32` `\text(Total) =2146` Finally, use the formula to compute for the mean.`\text(Mean)` `=` $$\frac{\color{#314EC4}{\sum f⋅c.c.}}{\color{#9202AA}{\sum f}}$$ Mean Formula `\text(Mean)` `=` $$\frac{\color{#314EC4}{2146}}{\color{#9202AA}{32}}$$ Substitute values `\text(Mean)` `=` `67.1` Rounded to one decimal place `\text(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.`\text(Class)` `\text(Class Centre) (c.c.)` `\text(Frequency) (f)` `04` `2` `5` `59` `7` `9` `1014` `12` `13` `1519` `17` `10` `2024` `22` `7` `2529` `27` `2` `\text(Total) =46`  `\text(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 04 2 5 5 59 7 9 5+9=14 1014 12 13 14+13=27 1519 17 10 27+10=37 2024 22 7 37+7=44 2529 27 2 44+2=46 `\text(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 `23`rd and `24`th scores.Find the row that includes the `23`rd and `24`th scores.Class Class Centre `(c.c.)` Frequency `(f)` Cumulative Frequency 04 2 5 5 59 7 9 5+9=14 1014 12 13 14+13=27 1519 17 10 27+10=37 2024 22 7 37+7=44 2529 27 2 44+2=46 `\text(Total) =46` The third row covers all scores between the `15`th and `27`th position — this includes the `23`rd and `24`th.Since we are looking for the median class, it will be the class where the two scores are located, which is `1014`.`\text(Median Class)=1014` 
Question 6 of 6
6. Question
The mass of `32` students was measured and the results are shown. Find the median class.`\text(Class)` `\text(Class Centre) (c.c.)` `\text(Frequency) (f)` `5155` `53` `1` `5660` `58` `4` `6165` `63` `8` `6670` `68` `10` `7175` `73` `6` `7680` `78` `2` `8185` `83` `1` `\text(Total) =32`  `\text(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 5155 53 1 1 5660 58 4 1+4=5 6165 63 8 5+8=13 6670 68 10 13+10=23 7175 73 6 23+6=29 7680 78 2 29+2=31 8185 83 1 31+1=32 `\text(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 `16`th and `17`th scores.Find the row that includes the `16`rd and `17`th scores.Class Class Centre `(c.c.)` Frequency `(f)` Cumulative Frequency 5155 53 1 1 5660 58 4 1+4=5 6165 63 8 5+8=13 6670 68 10 13+10=23 7175 73 6 23+6=29 7680 78 2 29+2=31 8185 83 1 31+1=32 `\text(Total) =32` The fourth row covers all scores between the `14`th and `23`rd position — this includes the `16`th and `17`th.Since we are looking for the median class, it will be the class where the two scores are located, which is `6670`.`\text(Median Class)=6670`
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