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Create and Interpret Bar & Line Graphs (Histograms)Create and Interpret Bar & Line Graphs (Histograms)
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Question 1 of 6
1. Question
From the frequency histogram shown below, find the mode of the scores.
- `\text(Mode )=` (4)
Hint
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A histogram is a bar graph version of the frequency distribution table.The mode is the value that appears most often in a set of data.First, convert the histogram into a frequency table.Score `(x)` – values at the bottom of the histogramFrequency `(f)` – height of each bar on the histogramScore `(x)` Frequency `(f)` 1 2 2 8 3 16 4 20 5 12 6 4 7 2 Notice that the highest value in the Frequency column is `20` and it corresponds to `4`.Score `(x)` Frequency `(f)` 1 2 2 8 3 16 4 20 5 12 6 4 7 2 In other words, the score `4` occurs the most frequently, and is therefore the mode.`\text(Mode)=4` -
Question 2 of 6
2. Question
From the frequency histogram shown below, find the mean of the scores.
Round your answer to two decimal places- `\text(Mean )=` (3.81)
Hint
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Mean Formula
$$\text{Mean}=\frac{\color{#314EC4}{\sum f⋅x}}{\color{#9202AA}{\sum f}}$$Remember
A histogram is a bar graph version of the frequency distribution table.First, convert the histogram into a frequency table.Score `(x)` – values at the bottom of the histogramFrequency `(f)` – height of each bar on the histogram`f⋅x` – sum of `x` and `f` on each row in the newly created frequency table.Score `(x)` Frequency `(f)` `f⋅x` 1 2 2 2 8 16 3 16 48 4 20 80 5 12 60 6 4 24 7 2 14 Find the sum of both the Frequency and `f.x` columns.`sum f` `=` `2+8+16+20+12+4+2` `=` `64` `sum f⋅x` `=` `2+16+48+80+60+24+14` `=` `244` Score `(x)` Frequency `(f)` `f⋅x` 1 2 2 2 8 16 3 16 48 4 20 80 5 12 60 6 4 24 7 2 14 `\text(Total) =64` `\text(Total) =244` Use the formula to compute for the mean.`\text(Mean)` `=` $$\frac{\color{#314EC4}{\sum f⋅x}}{\color{#9202AA}{\sum f}}$$ Mean Formula `\text(Mean)` `=` $$\frac{\color{#314EC4}{244}}{\color{#9202AA}{64}}$$ Substitute values `\text(Mean)` `=` `3.81` Rounded to two decimal places `\text(Mean)=3.81` -
Question 3 of 6
3. Question
From the frequency histogram shown below, find the median of the scores.
- `\text(Median )=` (4)
Hint
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A histogram is a bar graph version of the frequency distribution table.The median is the middle value of a data set.If there are two middle values on a data set, we get their sum and halve it to get the median.First, convert the histogram into a frequency table.Score `(x)` – values at the bottom of the histogramFrequency `(f)` – height of each bar on the histogramScore `(x)` Frequency `(f)` 1 2 2 8 3 16 4 20 5 12 6 4 7 2 Find the sum of both the Frequency and `f.x` columns.`sum f` `=` `2+8+16+20+12+4+2` `=` `64` Score `(x)` Frequency `(f)` 1 2 2 8 3 16 4 20 5 12 6 4 7 2 `\text(Total) =64` Next, arrange the values of the data set in ascending orderThe frequency `(f)` indicates how many times a score should be listed`1` `1` `2` `2` `2` `2` `2` `2` `2` `2` `3` `3` `3` `3` `3` `3` `3` `3` `3` `3` `3` `3` `3` `3` `3` `3` `4` `4` `4` `4` `4` `4` `4` `4` `4` `4` `4` `4` `4` `4` `4` `4` `4` `4` `4` `4` `5` `5` `5` `5` `5` `5` `5` `5` `5` `5` `5` `5` `6` `6` `6` `6` `7` `7` We can see that the values `4` and `4` are the middle values of the data set.To find the median, we add the two middle values and divide it by `2``\text(Median)` `=` `(4+4)/2` `=` `8/2` `=` `4` `\text(Median)=4` -
Question 4 of 6
4. Question
A group of `17` students were surveyed as to how many phone calls they made on the weekend. Draw a frequency distribution table and then a histogram.`10` `8` `12` `9` `10` `6` `10` `9` `9` `11` `7` `9` `6` `9` `11` `8` `10` Hint
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A frequency distribution table displays how many times a particular score has occurred in a set of data.A histogram is a bar graph version of the frequency distribution table.First, fill in the Score column with the range of all possible scores, in ascending order.Score `(x)` Tally Frequency `(f)` 6 7 8 9 10 11 12 `\text(Total) =` Next, read across the data while placing a stroke in the Tally column for each corresponding score.
To reduce the chance of mistakes, cross off each score as they are tallied.`10` `8` `12` `9` `10` `6` `10` `9` `9` `11` `7` `9` `6` `9` `11` `8` `10` Score `(x)` Tally Frequency `(f)` 6 7 8 9 10 11 12 `\text(Total) =` Continue doing this until all scores are tallied.Score `(x)` Tally Frequency `(f)` 6 7 8 9 10 11 12 `\text(Total) =` Count the tallies per score and note it under the Frequency column.Score `(x)` Tally Frequency `(f)` 6 2 7 1 8 2 9 5 10 4 11 2 12 1 `\text(Total) =` To check, count the total frequency and make sure it is equal to the number of given scores.Score `(x)` Tally Frequency `(f)` 6 2 7 1 8 2 9 5 10 4 11 2 12 1 `\text(Total) =17` From the given data, we know that `N=17`Therefore, all scores have been accounted for.Now, for the histogram, prepare a bar graph with the scores listed at the bottom, and the frequency listed at the left side.
For each score, draw a bar with height corresponding to the frequency of that score.
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Question 5 of 6
5. Question
From the frequency polygon shown below, find the mean of the scores.
Round your answer to one decimal place- `\text(Mean )=` (5.6)
Hint
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Mean Formula
$$\text{Mean}=\frac{\color{#314EC4}{\sum f⋅x}}{\color{#9202AA}{\sum f}}$$Remember
A frequency polygon is a line graph version of the frequency distribution table.First, convert the frequency polygon into a frequency table.Score `(x)` – values at the bottom of the histogramFrequency `(f)` – height of each bar on the histogram`f⋅x` – sum of `x` and `f` on each row in the newly created frequency table.Score `(x)` Frequency `(f)` `f⋅x` 2 3 6 3 2 6 4 5 20 5 6 30 6 9 54 7 12 84 8 3 24 Find the sum of both the Frequency and `f.x` columns.`sum f` `=` `3+2+5+6+9+12+3` `=` `40` `sum f⋅x` `=` `6+6+20+30+54+84+24` `=` `224` Score `(x)` Frequency `(f)` `f⋅x` 2 3 6 3 2 6 4 5 20 5 6 30 6 9 54 7 12 84 8 3 24 `\text(Total) =40` `\text(Total) =224` Use the formula to compute for the mean.`\text(Mean)` `=` $$\frac{\color{#314EC4}{\sum f⋅x}}{\color{#9202AA}{\sum f}}$$ Mean Formula `\text(Mean)` `=` $$\frac{\color{#314EC4}{224}}{\color{#9202AA}{40}}$$ Substitute values `\text(Mean)` `=` `5.6` `\text(Mean)=5.6` -
Question 6 of 6
6. Question
From the frequency polygon shown below, construct a frequency distribution table and determine how many fishermen are in the group.
Enter the frequency for each respective score in the table below-
Score `(x)` Frequency `(f)` 2 (3) 3 (2) 4 (5) 5 (6) 6 (9) 7 (12) 8 (3) `\text(Total) =`
Hint
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A frequency distribution table displays how many times a particular score has occurred in a set of data.This frequency polygon can be expressed as:Hours fishing `=` Score `(x)` No. of fishermen `=` Frequency `(f)` Name the table accordingly, then fill in the Hours fishing column with the values at the bottom of the polygon.Hours fishing `(x)` No. of fishermen `(f)` 2 3 4 5 6 7 8 `\text(Total) =` Next, check the points on the polygon and note the corresponding No. of fishermen for each Hours fishing under the No. of fishermen column.Hours fishing `(x)` No. of fishermen `(f)` 2 3 3 2 4 5 5 6 6 9 7 12 8 3 `\text(Total) =` Lastly, count the total frequency.Hours fishing `(x)` No. of fishermen `(f)` 2 3 3 2 4 5 5 6 6 9 7 12 8 3 `\text(Total) =40` Hours fishing `(x)` No. of fishermen `(f)` 2 3 3 2 4 5 5 6 6 9 7 12 8 3 `\text(Total) =40` -
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