- In order to draw meaningful inferences from a given data set, we need to organize the data systematically and then display it visually.
- Line plots, box plots, histograms, stem-and-leaf plots, and circle plots are some of the ways to visualize data for easier analysis of the data set.
- A line plot is a way to graphically display a given data set on a number line.
- The horizontal line (number line) shows the categories being considered.
- The frequency corresponding to each category is displayed using dots, crosses, or any other symbol over them.
- In the line plot shown below, the number line displays the time taken by students to complete a test (in minutes) and the "circle" mark represents the number of students (frequency).
- A box plot is a way to display the distribution of a given data set.
- Box plot displays five key parameters about a data set as mentioned below:
- the minimum value,
- the first quartile ,
- the third quartile , and
- the maximum value
- We can also compute the range and interquartile range (IQR) of a given data set from the box plot.
- A histogram is a graphical display of continuous numerical data distribution (just like bar graphs are used to represent categorical data).
- The horizontal axis of a histogram represents the class interval (bins) while the height of each bin displays the frequency of data values in that interval.
- Recall that frequency means the number of times a particular entry occurs.
- The histogram shown below displays the weekly self-study duration of some of the students in Grade 7.
- It should be noted that the width of the bins is equal.
- A histogram also displays whether the distribution is skewed or symmetric.
- A stem and leaf plot is a way to organize and display data in a special table.
- Each data value is broken into a stem and a leaf.
- The 'stem' is on the left side of the table & displays the first digit or digits of the data.
- The 'leaf' is on the right side of the table & displays the last digit.
- The stem and leaf plot key at the bottom of the table helps us understand the data values.
- If we combine the values of the stem and the leaves (as per the rule indicated by the key), we will get the data values.
- For example, the stem and leaf plot shown below represents the age of people who watched a particular movie on Sunday in City Mall.
- A circle graph aka Pie Chart is used to visualize data (as a fractional part of a whole) on a circle.
- In a circle graph, the area of a circle is divided into slices to display the numerical proportion of each category.
- Each angle of the circle graph is proportional to the quantity it represents.
- Percentage of a category =
- The angle subtended by a category =
- The pie chart shown below exhibits the distribution of favorite games of the population of residents of New York City.
Question 1: The line plot shown below represents the time taken by some of the university students to complete a bike race. Find the mean and median time taken to complete the race.
Median = value of middlemost observation after arranging the data in ascending/descending order
There are 20 data values. The Median will be the average of & value.
Question 2: The stem-and-leaf plot shown below represents the scores of 25 students on a test (out of 50 marks). Find the mode score.
Solution: Mode is the data that occurs most frequently in a given data set. It can be clearly seen from the stem-and-leaf plot that a score of 35 occurs most frequently (6 times), and hence 35 is the mode score.
Question 3: The box plot shown below represents the duration (in hours) of TV watched by some students in a given month. Determine the median of watch time.
Solution: Median = value of middlemost observation after arranging the data in ascending/descending order
From the given plot, it is clearly evident that the median watch time is 35 hours.
Question 4: The marks scored by 100 students of Grade 7 in the Mathematics test (out of 50) was recorded and displayed in the histogram shown below. If a student scores 20 and above, he is declared as 'qualified'. Find the number of students who did not qualify for the test.
Solution: From the histogram shown above, the number of students who could not qualify for the test = 5 + 15 = 20.
Question 5: The circle chart shown below represents the expenditure on various items by an international student in Florida. If his total monthly expenditure is $1,900, find the money spent on food.
Solution: Total monthly expenditure = $1,900.
Expenditure on food =
- A line plot is drawn on a number line that represents categories and the frequency of data points corresponding to each category is displayed above it using dots, crosses, or any other symbol.
- Through a box plot, we get information regarding 5 key parameters of a dataset - the minimum value, first quartile, median, third quartile, and maximum value.
- A histogram is a type of bar graph, where the class intervals are shown on the horizontal axis and the heights of the bars display the frequency of the class interval.
- In a stem-and-leaf plot, each data point is split into two components - a stem and a leaf. Combining the satem and leaf data using a predefined key gives back the original data point.
- A circle graph shows the relationship between a whole and its part.
- It is good practice to identify outliers before drawing charts. This is because the presence of outliers can have a disproportionate effect on the statistical results. (the results can be misleading).