7th Grade - Graphs and Charts

Introduction

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 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 $(Q_{1})$ ,
- median,
- the third quartile $(Q_{3})$ , 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: $Q_{3} - Q_{1}$

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 = $\frac{A m o u n t i n c a t e g o r y}{t o t a l} \times 100$
The angle subtended by a category = $\frac{A m o u n t i n c a t e g o r y}{t o t a l} \times 360 °$
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: $Mean = \frac{S u m o f a l l t h e o b s e r v a t i o n s}{T o t a l n u m b e r o f o b s e r v a t i o n s}$

$= \frac{(12 \times 1) + (13 \times 2) + (14 \times 3) + (15 \times 4) + (16 \times 1) + (17 \times 1) + (18 \times 3) + (19 \times 2) + (20 \times 1) + (21 \times 2)}{(1 + 2 + 3 + 4 + 1 + 1 + 3 + 2 + 1 + 2)}$

$= \frac{327}{20}$

$= 16.35 minutes$

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 $10^{t h}$ & $11^{t h}$ value.

$Median = \frac{17 + 18}{2} = 17.5$

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 = $8 % of 1, 900$ $= \frac{8}{100} \times 1, 900$ $= $ 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 outliers can have a disproportionate effect on the statistical results (the results can be misleading).

7th Grade - Graphs and Charts

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