7th Grade - Graphs and Charts

Introduction

  • 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.

Line Plots

  • 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).

 

Box Plots

  • 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 Q1,
    • median,
    • the third quartile Q3, and
    • the maximum value

  • We can also compute the range and interquartile range (IQR) of a given data set from the box plot.
    • Range: maximum value - minimum value
    • IQR: Q3-Q1

Histograms

  • 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.

Stem-and-Leaf Plot

  • 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.

Circle Graph (Pie Chart)

  • 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 = Amount in categorytotal×100
  • The angle subtended by a category = Amount in categorytotal×360°
  • The pie chart shown below exhibits the distribution of favorite games of the population of residents of New York City.

 

Solved Examples

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.

Solution: Mean = Sum of all the observationsTotal number of observations

=12×1+13×2+14×3+15×4+16×1+17×1+18×3+19×2+20×1+21×21+2+3+4+1+1+3+2+1+2

=32720

=16.35 minutes

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 10th & 11th value.

Median = 17+182=17.5

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 = 8% of 1,900=8100×1,900=$152

Cheat Sheet

  • 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.

Blunder Areas

  • 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).