our logo - study4details

comprehensive study approach

Tag: statistics

  • Introduction to statistics

    Introduction to statistics

    Introduction to statistics will guide us on the basic concepts as used in statistics.  Statistics is the science of data collection, organization, representation and interpretation of data or information. It plays a vital role in decision-making across various fields, including business, economics, science, and social sciences. The topic is divided into two main areas: descriptive statistics and inferential statistics.

    1. Descriptive statistics involves summarizing and organizing data. Introduction to statistics will expose us to tools include mean, median, mode, and standard deviation. Graphical representations like histograms and pie charts are also used. It helps in understanding the basic features of data.
    2. Inferential statistics focuses on making predictions or inferences about a population based on a sample. Techniques like hypothesis testing, confidence intervals, and regression analysis are used to estimate population parameters and test assumptions.

    Statistics also includes the study of probability, which underpins many statistical methods by assessing the likelihood of events. Overall, statistics is crucial for making informed decisions and understanding patterns in data.

    Please note the difference between statistics and statistic.

    Statistic

    Statistic is a collection of information shown in numbers. For example the number of people that browse a a web in a day is a statistic.

    introduction to statistics: Data as used in statistics

    Data is used to mean fact or information which needs examination or processing to extract useful information. For example counting the number of people in a location is data collection. Data collection is described as gathering of facts that are used for information processing.

    Examples of data collections include:

    • The number of items sold per category of items sold in the supermarket
    • The number of crimes or cases reported to a police station daily
    • The average fuel consumption of a country in a month
    • Number of people infected with HIV virus per day
    • The average rainfall of an area over a given period

    Introducing statistics : Data representation

    Data collected should be presented in a way that is most useful to the consumer. This means it should be represented in a way that is convenient and easy to understand. Data that is well represented will be understood and be interpreted easily.

    Some of the techniques used to represent data includes

    • Listing the data in a chronological order
    • pictograms (picture graphs)
    • bar charts
    • pie charts
    • histograms
    • Frequency tables

    Listing of data

    Listing data is simply putting down the actual numbers representing a quantity of an item in a data set. for example consider a class of 20 students that are in a computer science class that sits for a test and scored the following marks in percentage:

    82, 70, 79, 61, 56, 67, 80, 60, 55, 62, 65, 73,74, 76, 67, 78, 83, 68, 59, 49.

    Above represents a list of marks as recorded by the teacher from the students scripts. A list of numbers is not very useful on its own. However, we can make it more meaningful by arranging the items in ascending or descending order.

    From the ordered list, one can determine the highest value and the smallest value. One can also find the value that is repeated most often. Additionally, you can identify the value that is in the middle.

    If you can consider the data above, it’s ordered list will be as follow:

    49, 55, 56, 59, 60, 61, 62, 65, 67, 67, 68, 70, 73, 74, 76, 78, 79, 80, 82, 83.

    The lowest value is at the beginning of the list. The largest value is at the end of the list. As you can see from the list.

    Please note that the value that are repeated are placed next to each other.

    To get to the middle we simple divide the list size by two. For example, in the above list, we find the middle by getting a value between the 10th and 11th positions. We will be talking more about the mid value in the upcoming lessons.

    Exercise 1

    Marks scored in an English test by a group of 17 students were recorded. The total was out of 30 possible marks.

    17, 18, 12, 13, 15, 14, 17, 23, 14, 27, 24, 16, 23, 14, 21, 14, 13.

    1. List the scores in ascending order
    2. which is the most common score
    3. how many scores above the common score
    4. what is the difference between the largest and smallest value
    5. what significance can you draw from number 4 above
    6. which score is in the middle.

    Click to see Answers

    statistics symbols

    Frequency tables

    Frequency means the number of times a value is recorded or observed. It means the count of a particular value in a data set.

    A tally mark (/) is made for every occurrence of an item while counting the scores. Every 5th occurrence is stroked across the other four ////. The result of tallying is placed on a table. The value makes one column. Tallying is another column. The frequency is another column. From the table, much more manipulation of data can be done. We are likely to see that in other lessons.

    Data Manipulation in statistics

    consider the data below:

    82, 70, 79, 61, 56, 67. 80, 60, 67. 55, 62, 65. 73, 74, 76. 67, 78, 83. 68, 59, 67. 49, 64, 80. 79, 60, 55. 73, 73, 67. 74, 61, 73. 82, 83, 73, 67.

    We will make a table of three columns. In the first column, we will list every unique value that is represented in the data. The second column we will put the tallying and the third column we put the result of the tallying.

    MarkTallyingFrequency
    49/1
    55//2
    56/1
    59/1
    60//2
    61//2
    62/1
    64/1
    65/1
    67//// /6
    68/1
    70/1
    73////5
    74//2
    76/1
    78/1
    79//2
    80//2
    82//2
    83//2
    Total37

    A frequency distribution table

    Exercise 2

    The next are scores in a math class for 21 students :

    35, 30, 27, 29, 32, 31, 28, 27, 29, 30, 31, 29, 29, 34, 29, 30,27, 28,31, 31, 3035, 30, 27, 29, 32, 31, 28, 27, 29, 30, 31, 29, 29, 34, 29, 30,27, 28,31, 31, 30

    1. Arrange the data in descending order
    2. Make a frequency table for the data
    3. What is the most common mark

    Related Topics

  • Bar Graphs

    Bar Graphs

    Bar graphs constitutes vertical or horizontal rectangles drawn on a Cartesian plane in order to represent a particular data item with it’s frequency.

    Bar charts are especially effective when you have numerical data that splits nicely into different categories so you can quickly see trends within your data.  They are best used to:

    • show change over time
    • compare different categories
    • compare parts of a whole.

    There are two types of simple bar charts:

    • Vertical or column chart –bars are moving upwards or are vertical.
    • Horizontal bar chart– This is a bar chart where the bars are horizontal.

    For vertical bar graphs, horizontal axis represents category of items and vertical axis the frequency.

    For horizontal bar graphs, item categories are on vertical axis and frequency on the horizontal axis. see the figure below

    Bar graphs are particularly useful in making comparison of data.The height or length of a bar graph is directly proportional to frequency but the width does not have numerical significance.

    As an example consider a hypothetical data about daily visitors that calls in in the first seven major stores in Washington as in table below.

    We can represent the above information on a bar graph for a more appealing visualization. A typical vertical bar graph for the above data can be as in the diagram below.

    A vertical bar graph

    If the same information could be represented using horizontal bar graph, it could appear as shown below:

    Horizontal bar graph

    Each unit in the horizontal scale represents 200 visitors

    By now you may have realized that a chart has 5 important elements:

    • Chart title– example: Number of visitors per day in 5 stores
    • Vertical axis title-e.g : store name
    • horizontal axes title-e.g : number of visitors
    • axes labels-e.g, Amazon fresh, Food lion, Gian….
    • data labels

    Chart title is arguably the most important piece of a chart.It is the element that lets the audience know what your chart is about.

    Your chart titles should be descriptive enough such that, at first glance, your audience knows what information the chart intends to give them. The title should also be brief and concise so that the graph is not cluttered.

    Chart title is usually placed at the top of the chart.

    Example

    The table below shows the number of students enrolled in each course in the department of Science and Engineering at Kenyatta University on January 2024.

    Draw a bar graph to show this information

    solution

    Vertical bar chart showing relationship between enrollment and course

    The vertical scale in the above chart represents 1 unit for 5 students

    Multiple Bar Graphs

    Multiple bar graphs are used when we have more than one category of data entities to analyse. For example performance of students in two or more subjects.

    For Example compare sales value of two loan products for various banks in the last one year in million dollars as shown

    Task: draw a bar graph to represent this information

    Solution

    Multiple bar graphs

    In the above chart the bar blue bar represents A mortgage sales and the orange colour represents business loan.

    Divided Bar Charts

    This are bar charts that represents two or more quantities on the same bar where one category is connected in series with the other category.

    The information about bank products described above could be represented as stacked graph as shown.

    stacked bar graphs

    Practice Exercise

    1. The table below shows the number of female and male students enrolled in 7 courses offered in a semester from the department of science and Technology.

    Task:

    1. Draw a multiple graph to represent the information
    2. Draw a stacked graph to represent the information
    3. Which causes has more females compared to males
    4. which cause has the lowest number of participants

    2. Learners in grade 4 were asked to name breed of dogs at their home and their teacher recorded their response in the table below.

    Required: Represent the data on a bar graph.

    3. The results of a mathematics tests for 30 students were as follows:

    43 62 33 45 56 32 34 39 51 65 32 43 33 32 43 45 46 44 33 45 51 56 35 33 34 45 32 42 43 62

    Required: Make a bar graph to show this information

    4. The masses of students in grade 7 and 8 were recorded as follow

    required:

    1. draw a multiple bar graphs to represent this information
    2. Represent the information using a stacked graph

    Conclusion

    In this lesson we have discussed how to represent data Using bar graphs. Bar graphs represents data in a more intuitive way. There are various ways we can draw bar graphs. This includes:

    • Vertical bar graphs
    • Horizontal bar graphs
    • Multiple bar graphs
    • stacked bar graphs

    We can compare more than one entity of data in one bar graph.

    Related Topics

  • Statistics

    Statistics

    Statistics is the science of data collection, organization, representation and interpretation of data or information.

    Please note the difference between statistics and statistic.

    Statistic

    Statistic is a collection of information shown in numbers. For example the number of people that browse a a web in a day is a statistic.

    Data

    Data is used to mean fact or information which needs examination or processing in order to extract useful information. For example counting the number of people in a location is data collection. Data collection may be described as gathering of facts that may be used for information processing.

    Examples of data collections may include:

    • The number of items sold per category of items sold in the supermarket
    • The number of crimes or cases reported to a police station daily
    • The average fuel consumption of a country in a month
    • Number of people infected with HIV virus per day
    • The average rainfall of an area over a given period

    Data representation

    Data collected should be presented in a way that is most useful to the consumer meaning it should be represented in a way that is convenient and easy to understand. Data that is well represented will be understood and be interpreted easily.

    Some of the methods used to represent data includes

    • Listing the data in a chronological order
    • pictograms (picture graphs)
    • bar charts
    • pie charts
    • histograms
    • Frequency tables

    Listing of data

    Listing data is simply putting down the actual numbers representing a quantity of an item in a data set. for example consider a class of 20 students that are in a computer science class that sits for a test and scored the following marks in percentage:

    82, 70, 79, 61, 56, 67, 80, 60, 55, 62, 65, 73,74, 76, 67, 78, 83, 68, 59, 49.

    Above represents a list of marks as recorded by the teacher from the students scripts. There is nothing much we can do with a list of numbers, but we can make the list more meaningful by arranging the items in ascending or descending orders.

    From the ordered list, one can determine the highest value, smallest value, a value that is repeated most of times and the value that is at the middle.

    If you can consider the data above, it’s ordered list will be as follow:

    49, 55, 56, 59, 60, 61, 62, 65, 67, 67, 68, 70, 73, 74, 76, 78, 79, 80, 82, 83.

    As you can see from the list, the lowest value is at the beginning of the list and the largest value is at the end of the list.

    Please note that the value that are repeated are placed next to each other.

    To get to the middle we simple divide the list size by two. for example in the above list, to get to the middle we simple gets a value between 10th and 11th position. We will be talking more about the mid value in the upcoming lessons.

    Exercise 1

    Marks scored in an English test by a group of 17 students were recorded as follows out of 30 possible marks.

    17, 18, 12, 13, 15, 14, 17, 23, 14, 27, 24, 16, 23, 14, 21, 14, 13.

    1. List the scores in ascending order
    2. which is the most common score
    3. how many scores above the common score
    4. what is the difference between the largest and smallest value
    5. what significance can you draw from number 4 above
    6. which score is in the middle.
    Click to see Answers
    statistics symbols

    Frequency tables

    Frequency means the number of times a value is recorded or observed. It means the count of a particular value in a data set.

    While counting the scores, a tally mark / is made for every occurrence of an item and every 5th occurrence is stroked across the other four ////. The result of tallying is placed on a table with the value making one column, tallying another column and the frequency another column. From the table, much more manipulation of data can be done, but we are likely to see that in other lessons.

    consider the data below:

    82, 70, 79, 61, 56, 67, 80, 60, 67, 55, 62, 65, 73, 74, 76, 67, 78, 83, 68, 59, 67, 49, 64, 80, 79, 60, 55, 73, 73, 67, 74, 61, 73, 82, 83, 73, 67.

    We will make a table of three columns and in the first column we list every unique value that is represented in the data . The second column we will put the tallying and the third column we put the result of the tallying

    MarkTallyingFrequency
    49/1
    55//2
    56/1
    59/1
    60//2
    61//2
    62/1
    64/1
    65/1
    67//// /6
    68/1
    70/1
    73////5
    74//2
    76/1
    78/1
    79//2
    80//2
    82//2
    83//2
    Total37
    A frequency distribution table

    Exercise 2

    The following are scores in a math class for 21 students :

    35, 30, 27, 29, 32, 31, 28, 27, 29, 30, 31, 29, 29, 34, 29, 30, 27, 28, 31, 31, 30.

    1. Arrange the data in descending order
    2. Make a frequency table for the data
    3. What is the most common mark

    Related Topics