Receiving Helpdesk

how do you find the class boundaries in a frequency distribution

by Randi Kerluke Published 3 years ago Updated 2 years ago

Use the following steps to calculate the class boundaries:

  1. Subtract the upper class limit for the first class from the lower class limit for the second class. ...
  2. Divide the result by two. Next, we divide the result by 2. So, we get 0.1/2 = 0.05.
  3. Subtract the result from the lower class limit and add the result to the the upper class limit for each class.

Use the following steps to calculate the class boundaries:
  1. Subtract the upper class limit for the first class from the lower class limit for the second class. ...
  2. Divide the result by two. ...
  3. Subtract the result from the lower class limit and add the result to the the upper class limit for each class.
Jan 11, 2021

What are class boundaries in frequency tables?

Class Boundaries – Definition, Examples | How to find Class Boundaries in a Frequency Table? Class Boundaries are the data values that separate classes. These are not part of the classes or the data set. The class boundary is the middle point of the upper-class limit of one class and the lower class limit of the subsequent class.

How to calculate the class boundaries?

Follow the below-listed steps to calculate the Class Boundaries easily. They are along the lines Subtract the upper class limit for the first class from the lower class limit for the second class. Divide the result by two. Subtract the result from the lower class limit and add the result to the upper class limit for each class.

What are class limits in a frequency distribution?

In a frequency distribution, class limits represent the smallest and largest data values that can belong to each class. Each class in a frequency distribution has a lower class limit and an upper class limit: Lower class limit: The smallest data value that can belong to a class.

How do you calculate upper and lower class boundaries in Excel?

On the other hand, the upper boundary of each class is calculated by adding half of the gap value 1 2 = 0.5 1 2 = 0.5 to the class upper limit. Simplify the lower and upper boundaries columns. Add the lower and upper class boundaries columns to the original table.

What is class boundaries in frequency distribution?

Class boundaries: There is a space between the upper limit of one class and lower limit of the. next class. The halfway points of these intervals are called class boundaries.

How is class boundary determined?

Class boundaries. The lower class boundary of a given class is obtained by averaging the upper limit of the previous class and the lower limit of the given class. The upper class boundary of a given class is obtained by averaging the upper limit of the class and the lower limit of the next class.

How do you find the class boundaries and class width?

Class width refers to the difference between the upper and lower boundaries of any class (category)....To find the width:Calculate the range of the entire data set by subtracting the lowest point from the highest,Divide it by the number of classes.Round this number up (usually, to the nearest whole number).

What are the class boundaries of the class?

What are Class Boundaries? Class boundaries are the data values which separate classes. They are not part of the classes or the dataset. The lower class boundary of a class is defined as the average of the lower limit of the class in question and the upper limit of the previous class.

How do you find class boundaries with decimals?

0:112:29How to Find the Class Boundaries in a Frequency Table with DecimalsYouTubeStart of suggested clipEnd of suggested clipHere. So first thing you do again is it just takes two numbers add them up divide by three to getMoreHere. So first thing you do again is it just takes two numbers add them up divide by three to get that and I comes there to get this number all you do is subtract the class width.

How do you find the lower class boundary of the median class?

0:076:44median for grouped data (ascending order) - YouTubeYouTubeStart of suggested clipEnd of suggested clipMinus the cumulative frequency of the lower class next to the median class divided by the frequency.MoreMinus the cumulative frequency of the lower class next to the median class divided by the frequency. Of the median class times the class width. Take note that the scores are grouped in six classes.

What is the class width for a frequency distribution with classes?

The class width is the difference between the upper or lower class limits of consecutive classes. All classes should have the same class width. In this case, class width equals to the difference between the lower limits of the first two classes. Simplify to find that the class width is 11 .

What is the class boundary of 10 19?

Each class thus has an upper and a lower class boundary. It must be noted that upper class boundary of one class and the lower class boundary of the subsequent class are the same....What is Class Boundary?ClassFrequency10 - 19520 - 2971 more row•May 29, 2013

Can class boundaries equal class limits?

In class limit, the upper extreme value of the first class interval and the lower extreme value of the next class interval will not be equal. In class boundary, the upper extreme value of the first class interval and the lower extreme value of the next class interval will be equal.

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z 1 2 3 4 5 6 7 8 9
8.3.21PHP Version3.92sRequest Duration2MBMemory UsageGET {post}Route
  • warninglog[00:33:39] LOG.warning: Creation of dynamic property Barryvdh\Debugbar\DataFormatter\QueryFormatter:...
  • warninglog[00:33:39] LOG.warning: Creation of dynamic property Barryvdh\Debugbar\DataFormatter\QueryFormatter:...
  • warninglog[00:33:39] LOG.warning: Callables of the form ["Swift_SmtpTransport", "Swift_Transport_EsmtpTranspor...
  • warninglog[00:33:39] LOG.warning: Creation of dynamic property Barryvdh\Debugbar\DataFormatter\SimpleFormatter...
  • warninglog[00:33:39] LOG.warning: Creation of dynamic property Barryvdh\Debugbar\DataFormatter\SimpleFormatter...
  • warninglog[00:33:39] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
  • warninglog[00:33:39] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
  • warninglog[00:33:39] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
  • warninglog[00:33:39] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
  • warninglog[00:33:39] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
  • warninglog[00:33:39] LOG.warning: json_decode(): Passing null to parameter #1 ($json) of type string is deprec...
  • Booting (12.1ms)
  • Application (3.91s)
  • 1 x Application (99.68%)
    3.91s
    1 x Booting (0.31%)
    12.10ms
    7 templates were rendered
    • themes.DevBlog.content.post (resources/views/themes/DevBlog/content/post.blade.php)34blade
      Params
      0
      post
      1
      postContent
      2
      author
      3
      updated_at
      4
      bing_rich_snippet_text
      5
      bing_rich_snippet_link
      6
      bing_related_keywords
      7
      google_related_keywords
      8
      bing_news_title
      9
      bing_news_description
      10
      bing_videos
      11
      bing_images
      12
      bing_search_result_title
      13
      bing_search_result_description
      14
      bing_search_result_url
      15
      bing_paa_questions
      16
      bing_paa_answers
      17
      bing_slider_faq_questions
      18
      bing_slider_faq_answers
      19
      bing_pop_faq_questions
      20
      bing_pop_faq_answers
      21
      bing_tab_faq_questions
      22
      bing_tab_faq_answers
      23
      google_faq_questions
      24
      google_faq_answers
      25
      google_rich_snippet
      26
      google_search_result
      27
      indexedArray
      28
      total_images
      29
      total_videos
      30
      settings
      31
      url_current
      32
      menus
      33
      sidebar
    • themes.DevBlog.layouts.master (resources/views/themes/DevBlog/layouts/master.blade.php)41blade
      Params
      0
      __env
      1
      app
      2
      errors
      3
      post
      4
      postContent
      5
      author
      6
      updated_at
      7
      bing_rich_snippet_text
      8
      bing_rich_snippet_link
      9
      bing_related_keywords
      10
      google_related_keywords
      11
      bing_news_title
      12
      bing_news_description
      13
      bing_videos
      14
      bing_images
      15
      bing_search_result_title
      16
      bing_search_result_description
      17
      bing_search_result_url
      18
      bing_paa_questions
      19
      bing_paa_answers
      20
      bing_slider_faq_questions
      21
      bing_slider_faq_answers
      22
      bing_pop_faq_questions
      23
      bing_pop_faq_answers
      24
      bing_tab_faq_questions
      25
      bing_tab_faq_answers
      26
      google_faq_questions
      27
      google_faq_answers
      28
      google_rich_snippet
      29
      google_search_result
      30
      indexedArray
      31
      total_images
      32
      total_videos
      33
      settings
      34
      url_current
      35
      menus
      36
      sidebar
      37
      i
      38
      __currentLoopData
      39
      loop
      40
      item
    • themes.DevBlog.panels.head (resources/views/themes/DevBlog/panels/head.blade.php)41blade
      Params
      0
      __env
      1
      app
      2
      errors
      3
      post
      4
      postContent
      5
      author
      6
      updated_at
      7
      bing_rich_snippet_text
      8
      bing_rich_snippet_link
      9
      bing_related_keywords
      10
      google_related_keywords
      11
      bing_news_title
      12
      bing_news_description
      13
      bing_videos
      14
      bing_images
      15
      bing_search_result_title
      16
      bing_search_result_description
      17
      bing_search_result_url
      18
      bing_paa_questions
      19
      bing_paa_answers
      20
      bing_slider_faq_questions
      21
      bing_slider_faq_answers
      22
      bing_pop_faq_questions
      23
      bing_pop_faq_answers
      24
      bing_tab_faq_questions
      25
      bing_tab_faq_answers
      26
      google_faq_questions
      27
      google_faq_answers
      28
      google_rich_snippet
      29
      google_search_result
      30
      indexedArray
      31
      total_images
      32
      total_videos
      33
      settings
      34
      url_current
      35
      menus
      36
      sidebar
      37
      i
      38
      __currentLoopData
      39
      loop
      40
      item
    • themes.DevBlog.panels.header (resources/views/themes/DevBlog/panels/header.blade.php)41blade
      Params
      0
      __env
      1
      app
      2
      errors
      3
      post
      4
      postContent
      5
      author
      6
      updated_at
      7
      bing_rich_snippet_text
      8
      bing_rich_snippet_link
      9
      bing_related_keywords
      10
      google_related_keywords
      11
      bing_news_title
      12
      bing_news_description
      13
      bing_videos
      14
      bing_images
      15
      bing_search_result_title
      16
      bing_search_result_description
      17
      bing_search_result_url
      18
      bing_paa_questions
      19
      bing_paa_answers
      20
      bing_slider_faq_questions
      21
      bing_slider_faq_answers
      22
      bing_pop_faq_questions
      23
      bing_pop_faq_answers
      24
      bing_tab_faq_questions
      25
      bing_tab_faq_answers
      26
      google_faq_questions
      27
      google_faq_answers
      28
      google_rich_snippet
      29
      google_search_result
      30
      indexedArray
      31
      total_images
      32
      total_videos
      33
      settings
      34
      url_current
      35
      menus
      36
      sidebar
      37
      i
      38
      __currentLoopData
      39
      loop
      40
      item
    • themes.DevBlog.panels.navbar (resources/views/themes/DevBlog/panels/navbar.blade.php)41blade
      Params
      0
      __env
      1
      app
      2
      errors
      3
      post
      4
      postContent
      5
      author
      6
      updated_at
      7
      bing_rich_snippet_text
      8
      bing_rich_snippet_link
      9
      bing_related_keywords
      10
      google_related_keywords
      11
      bing_news_title
      12
      bing_news_description
      13
      bing_videos
      14
      bing_images
      15
      bing_search_result_title
      16
      bing_search_result_description
      17
      bing_search_result_url
      18
      bing_paa_questions
      19
      bing_paa_answers
      20
      bing_slider_faq_questions
      21
      bing_slider_faq_answers
      22
      bing_pop_faq_questions
      23
      bing_pop_faq_answers
      24
      bing_tab_faq_questions
      25
      bing_tab_faq_answers
      26
      google_faq_questions
      27
      google_faq_answers
      28
      google_rich_snippet
      29
      google_search_result
      30
      indexedArray
      31
      total_images
      32
      total_videos
      33
      settings
      34
      url_current
      35
      menus
      36
      sidebar
      37
      i
      38
      __currentLoopData
      39
      loop
      40
      item
    • themes.DevBlog.panels.footer (resources/views/themes/DevBlog/panels/footer.blade.php)41blade
      Params
      0
      __env
      1
      app
      2
      errors
      3
      post
      4
      postContent
      5
      author
      6
      updated_at
      7
      bing_rich_snippet_text
      8
      bing_rich_snippet_link
      9
      bing_related_keywords
      10
      google_related_keywords
      11
      bing_news_title
      12
      bing_news_description
      13
      bing_videos
      14
      bing_images
      15
      bing_search_result_title
      16
      bing_search_result_description
      17
      bing_search_result_url
      18
      bing_paa_questions
      19
      bing_paa_answers
      20
      bing_slider_faq_questions
      21
      bing_slider_faq_answers
      22
      bing_pop_faq_questions
      23
      bing_pop_faq_answers
      24
      bing_tab_faq_questions
      25
      bing_tab_faq_answers
      26
      google_faq_questions
      27
      google_faq_answers
      28
      google_rich_snippet
      29
      google_search_result
      30
      indexedArray
      31
      total_images
      32
      total_videos
      33
      settings
      34
      url_current
      35
      menus
      36
      sidebar
      37
      i
      38
      __currentLoopData
      39
      loop
      40
      item
    • themes.DevBlog.panels.scripts (resources/views/themes/DevBlog/panels/scripts.blade.php)41blade
      Params
      0
      __env
      1
      app
      2
      errors
      3
      post
      4
      postContent
      5
      author
      6
      updated_at
      7
      bing_rich_snippet_text
      8
      bing_rich_snippet_link
      9
      bing_related_keywords
      10
      google_related_keywords
      11
      bing_news_title
      12
      bing_news_description
      13
      bing_videos
      14
      bing_images
      15
      bing_search_result_title
      16
      bing_search_result_description
      17
      bing_search_result_url
      18
      bing_paa_questions
      19
      bing_paa_answers
      20
      bing_slider_faq_questions
      21
      bing_slider_faq_answers
      22
      bing_pop_faq_questions
      23
      bing_pop_faq_answers
      24
      bing_tab_faq_questions
      25
      bing_tab_faq_answers
      26
      google_faq_questions
      27
      google_faq_answers
      28
      google_rich_snippet
      29
      google_search_result
      30
      indexedArray
      31
      total_images
      32
      total_videos
      33
      settings
      34
      url_current
      35
      menus
      36
      sidebar
      37
      i
      38
      __currentLoopData
      39
      loop
      40
      item
    uri
    GET {post}
    middleware
    web, checkdate
    as
    post.show
    controller
    App\Http\Controllers\Frontend\json_data\PostController@show
    namespace
    where
    file
    app/Http/Controllers/Frontend/json_data/PostController.php:18-166
    7 statements were executed3.89s
    • select * from `posts` where `published_at` <= '2025-06-05 00:33:39' and `slug` = 'how-do-you-find-the-class-boundaries-in-a-frequency-distribution' and `posts`.`deleted_at` is null limit 1
      2.07ms/app/Providers/RouteServiceProvider.php:54receivinghelpdeskask
      Metadata
      Bindings
      • 0. 2025-06-05 00:33:39
      • 1. how-do-you-find-the-class-boundaries-in-a-frequency-distribution
      Backtrace
      • 15. /app/Providers/RouteServiceProvider.php:54
      • 18. /vendor/laravel/framework/src/Illuminate/Routing/Router.php:842
      • 19. Route binding:39
      • 20. /vendor/laravel/framework/src/Illuminate/Pipeline/Pipeline.php:167
      • 21. /vendor/laravel/framework/src/Illuminate/Foundation/Http/Middleware/VerifyCsrfToken.php:78
    • select * from `json_post_contents` where `json_post_contents`.`post_id` = 205350 and `json_post_contents`.`post_id` is not null and `rewrite_id` = 0
      7.45msmiddleware::checkdate:30receivinghelpdeskask
      Metadata
      Bindings
      • 0. 205350
      • 1. 0
      Backtrace
      • 19. middleware::checkdate:30
      • 20. /vendor/laravel/framework/src/Illuminate/Pipeline/Pipeline.php:167
      • 21. /vendor/laravel/jetstream/src/Http/Middleware/ShareInertiaData.php:61
      • 22. /vendor/laravel/framework/src/Illuminate/Pipeline/Pipeline.php:167
      • 23. /vendor/laravel/framework/src/Illuminate/Routing/Middleware/SubstituteBindings.php:50
    • select * from `nova_menu_menus` where `slug` = 'header' limit 1
      670μs/vendor/outl1ne/nova-menu-builder/src/helpers.php:32receivinghelpdeskask
      Metadata
      Bindings
      • 0. header
      Backtrace
      • 15. /vendor/outl1ne/nova-menu-builder/src/helpers.php:32
      • 17. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 18. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:45
      • 19. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:261
      • 20. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
    • select * from `nova_menu_menu_items` where `nova_menu_menu_items`.`menu_id` = 1 and `nova_menu_menu_items`.`menu_id` is not null and `parent_id` is null order by `parent_id` asc, `order` asc, `name` asc
      470μs/vendor/outl1ne/nova-menu-builder/src/Models/Menu.php:35receivinghelpdeskask
      Metadata
      Bindings
      • 0. 1
      Backtrace
      • 19. /vendor/outl1ne/nova-menu-builder/src/Models/Menu.php:35
      • 20. /vendor/outl1ne/nova-menu-builder/src/helpers.php:33
      • 22. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 23. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:45
      • 24. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:261
    • select * from `nova_menu_menu_items` where `nova_menu_menu_items`.`parent_id` in (1) order by `order` asc
      270μs/vendor/outl1ne/nova-menu-builder/src/Models/Menu.php:35receivinghelpdeskask
      Metadata
      Backtrace
      • 24. /vendor/outl1ne/nova-menu-builder/src/Models/Menu.php:35
      • 25. /vendor/outl1ne/nova-menu-builder/src/helpers.php:33
      • 27. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 28. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:45
      • 29. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:261
    • select `id`, `post_title`, `slug` from `posts` where `status` = 'publish' and `posts`.`deleted_at` is null order by RAND() limit 10
      3.88s/app/View/Composers/SidebarView.php:22receivinghelpdeskask
      Metadata
      Bindings
      • 0. publish
      Backtrace
      • 14. /app/View/Composers/SidebarView.php:22
      • 15. /app/View/Composers/SidebarView.php:12
      • 16. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:124
      • 17. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:162
      • 20. /vendor/laravel/framework/src/Illuminate/View/Concerns/ManagesEvents.php:177
    • select * from `fake_users` where `fake_users`.`id` = 13132 limit 1
      560μsview::2dd102cf0462e89a4d4d8bc77355d767652bf9aa:15receivinghelpdeskask
      Metadata
      Bindings
      • 0. 13132
      Backtrace
      • 21. view::2dd102cf0462e89a4d4d8bc77355d767652bf9aa:15
      • 23. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:108
      • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 25. /vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69
      • 26. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:61
    App\Models\FakeUser
    1
    Outl1ne\MenuBuilder\Models\MenuItem
    1
    Outl1ne\MenuBuilder\Models\Menu
    1
    App\Models\JsonPostContent
    1
    App\Models\Post
    11
        _token
        IIgykXGos2lbpQilvaY5x3RQnWK793lmnCCn1EAi
        _previous
        array:1 [ "url" => "https://receivinghelpdesk.com/ask/how-do-you-find-the-class-boundaries-in-a-fr...
        _flash
        array:2 [ "old" => [] "new" => [] ]
        PHPDEBUGBAR_STACK_DATA
        []
        path_info
        /how-do-you-find-the-class-boundaries-in-a-frequency-distribution
        status_code
        200
        
        status_text
        OK
        format
        html
        content_type
        text/html; charset=UTF-8
        request_query
        []
        
        request_request
        []
        
        request_headers
        0 of 0
        array:24 [ "cf-ipcountry" => array:1 [ 0 => "US" ] "cf-connecting-ip" => array:1 [ 0 => "3.141.2.184" ] "cdn-loop" => array:1 [ 0 => "cloudflare; loops=1" ] "sec-fetch-site" => array:1 [ 0 => "none" ] "accept" => array:1 [ 0 => "text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7" ] "user-agent" => array:1 [ 0 => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)" ] "upgrade-insecure-requests" => array:1 [ 0 => "1" ] "sec-ch-ua-platform" => array:1 [ 0 => ""Windows"" ] "sec-ch-ua-mobile" => array:1 [ 0 => "?0" ] "sec-ch-ua" => array:1 [ 0 => ""Chromium";v="130", "HeadlessChrome";v="130", "Not?A_Brand";v="99"" ] "cache-control" => array:1 [ 0 => "no-cache" ] "pragma" => array:1 [ 0 => "no-cache" ] "sec-fetch-dest" => array:1 [ 0 => "document" ] "cf-ray" => array:1 [ 0 => "94a9b1070915a468-ORD" ] "accept-encoding" => array:1 [ 0 => "gzip, br" ] "priority" => array:1 [ 0 => "u=0, i" ] "sec-fetch-user" => array:1 [ 0 => "?1" ] "sec-fetch-mode" => array:1 [ 0 => "navigate" ] "cf-visitor" => array:1 [ 0 => "{"scheme":"https"}" ] "connection" => array:1 [ 0 => "close" ] "x-forwarded-proto" => array:1 [ 0 => "https" ] "x-forwarded-for" => array:1 [ 0 => "3.141.2.184, 172.69.17.134" ] "x-server-addr" => array:1 [ 0 => "154.12.239.204" ] "host" => array:1 [ 0 => "receivinghelpdesk.com" ] ]
        request_server
        0 of 0
        array:55 [ "USER" => "runcloud" "HOME" => "/home/runcloud" "SCRIPT_NAME" => "/ask/index.php" "REQUEST_URI" => "/ask/how-do-you-find-the-class-boundaries-in-a-frequency-distribution" "QUERY_STRING" => "" "REQUEST_METHOD" => "GET" "SERVER_PROTOCOL" => "HTTP/1.0" "GATEWAY_INTERFACE" => "CGI/1.1" "REDIRECT_URL" => "/ask/how-do-you-find-the-class-boundaries-in-a-frequency-distribution" "REMOTE_PORT" => "43476" "SCRIPT_FILENAME" => "/home/runcloud/webapps/ReceivingHelpDesk/ask/index.php" "SERVER_ADMIN" => "you@example.com" "CONTEXT_DOCUMENT_ROOT" => "/home/runcloud/webapps/ReceivingHelpDesk/" "CONTEXT_PREFIX" => "" "REQUEST_SCHEME" => "http" "DOCUMENT_ROOT" => "/home/runcloud/webapps/ReceivingHelpDesk/" "REMOTE_ADDR" => "172.69.17.134" "SERVER_PORT" => "80" "SERVER_ADDR" => "127.0.0.1" "SERVER_NAME" => "receivinghelpdesk.com" "SERVER_SOFTWARE" => "Apache/2.4.63 (Unix) OpenSSL/1.1.1f" "SERVER_SIGNATURE" => "" "LD_LIBRARY_PATH" => "/RunCloud/Packages/apache2-rc/lib" "PATH" => "/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin" "HTTP_CF_IPCOUNTRY" => "US" "HTTP_CF_CONNECTING_IP" => "3.141.2.184" "HTTP_CDN_LOOP" => "cloudflare; loops=1" "HTTP_SEC_FETCH_SITE" => "none" "HTTP_ACCEPT" => "text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7" "HTTP_USER_AGENT" => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)" "HTTP_UPGRADE_INSECURE_REQUESTS" => "1" "HTTP_SEC_CH_UA_PLATFORM" => ""Windows"" "HTTP_SEC_CH_UA_MOBILE" => "?0" "HTTP_SEC_CH_UA" => ""Chromium";v="130", "HeadlessChrome";v="130", "Not?A_Brand";v="99"" "HTTP_CACHE_CONTROL" => "no-cache" "HTTP_PRAGMA" => "no-cache" "HTTP_SEC_FETCH_DEST" => "document" "HTTP_CF_RAY" => "94a9b1070915a468-ORD" "HTTP_ACCEPT_ENCODING" => "gzip, br" "HTTP_PRIORITY" => "u=0, i" "HTTP_SEC_FETCH_USER" => "?1" "HTTP_SEC_FETCH_MODE" => "navigate" "HTTP_CF_VISITOR" => "{"scheme":"https"}" "HTTP_CONNECTION" => "close" "HTTP_X_FORWARDED_PROTO" => "https" "HTTP_X_FORWARDED_FOR" => "3.141.2.184, 172.69.17.134" "HTTP_X_SERVER_ADDR" => "154.12.239.204" "HTTP_HOST" => "receivinghelpdesk.com" "HTTPS" => "on" "REDIRECT_STATUS" => "200" "REDIRECT_HTTPS" => "on" "FCGI_ROLE" => "RESPONDER" "PHP_SELF" => "/ask/index.php" "REQUEST_TIME_FLOAT" => 1749063819.4697 "REQUEST_TIME" => 1749063819 ]
        request_cookies
        []
        
        response_headers
        0 of 0
        array:7 [ "content-type" => array:1 [ 0 => "text/html; charset=UTF-8" ] "cache-control" => array:1 [ 0 => "private, must-revalidate" ] "date" => array:1 [ 0 => "Wed, 04 Jun 2025 19:03:39 GMT" ] "pragma" => array:1 [ 0 => "no-cache" ] "expires" => array:1 [ 0 => -1 ] "set-cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6IkpMOEp5RzZrUWptOG03bTRzUjJLSkE9PSIsInZhbHVlIjoiaGtQcFVNU1ZWU21YanVUZWs2clJsVDRyMW0zNEdYN1hZbHRmOXAvaEVic2diamRRNGo4dTUreEJKc0h3b0dWTWZqWXNYVkVNV2ZUMVpXMHV5NC9YVEpZOUlLWkdiMTBxcTVNNkRTaFJHelVFVjlQZlRudXQzY3dXc2VmT0ZFL2siLCJtYWMiOiJiNmFmYWM3NjcxZDM3MGJiNGQ3NmQyYmVhNzVjMmE0ZTA4MGMxOGY4NjY1NjI4MmZjZWViY2I3M2QzNGViNzJjIiwidGFnIjoiIn0%3D; expires=Wed, 04-Jun-2025 21:03:43 GMT; Max-Age=7200; path=/; samesite=laxXSRF-TOKEN=eyJpdiI6IkpMOEp5RzZrUWptOG03bTRzUjJLSkE9PSIsInZhbHVlIjoiaGtQcFVNU1ZWU21YanVUZWs2clJsVDRyMW0zNEdYN1hZbHRmOXAvaEVic2diamRRNGo4dTUreEJKc0h3b0dWTWZqWXNYV" 1 => "askhelpdesk_session=eyJpdiI6IkZXNFFIVTRsVVVoak5nYzZ1TWNMb3c9PSIsInZhbHVlIjoiTkJ2YUd4c3NvZkVVUlExK0grazBWQnVBdEduOXVsYWJGSmNkcDBxTTNlQlBzTzIyUC9FbGtMRTNqYU40QitzR2tnQ2FKV0RQUVdBYlZ2cGZhK0RZbE9YeU83QkI0bXNDcWR4WXVjcHFKYXdYczBNeWtKbVlXS3ltVFlFR3VCUzUiLCJtYWMiOiIyZWY3NTdhMjdmZTEzMDY3OWNmYTYwNDA2ZjRlZDA3N2U4ODg5YzQyM2JlNDMyMWJjNGVkMzBlNjA5NzhlZmMwIiwidGFnIjoiIn0%3D; expires=Wed, 04-Jun-2025 21:03:43 GMT; Max-Age=7200; path=/; httponly; samesite=laxaskhelpdesk_session=eyJpdiI6IkZXNFFIVTRsVVVoak5nYzZ1TWNMb3c9PSIsInZhbHVlIjoiTkJ2YUd4c3NvZkVVUlExK0grazBWQnVBdEduOXVsYWJGSmNkcDBxTTNlQlBzTzIyUC9FbGtMRTNqYU40Qitz" ] "Set-Cookie" => array:2 [ 0 => "XSRF-TOKEN=eyJpdiI6IkpMOEp5RzZrUWptOG03bTRzUjJLSkE9PSIsInZhbHVlIjoiaGtQcFVNU1ZWU21YanVUZWs2clJsVDRyMW0zNEdYN1hZbHRmOXAvaEVic2diamRRNGo4dTUreEJKc0h3b0dWTWZqWXNYVkVNV2ZUMVpXMHV5NC9YVEpZOUlLWkdiMTBxcTVNNkRTaFJHelVFVjlQZlRudXQzY3dXc2VmT0ZFL2siLCJtYWMiOiJiNmFmYWM3NjcxZDM3MGJiNGQ3NmQyYmVhNzVjMmE0ZTA4MGMxOGY4NjY1NjI4MmZjZWViY2I3M2QzNGViNzJjIiwidGFnIjoiIn0%3D; expires=Wed, 04-Jun-2025 21:03:43 GMT; path=/XSRF-TOKEN=eyJpdiI6IkpMOEp5RzZrUWptOG03bTRzUjJLSkE9PSIsInZhbHVlIjoiaGtQcFVNU1ZWU21YanVUZWs2clJsVDRyMW0zNEdYN1hZbHRmOXAvaEVic2diamRRNGo4dTUreEJKc0h3b0dWTWZqWXNYV" 1 => "askhelpdesk_session=eyJpdiI6IkZXNFFIVTRsVVVoak5nYzZ1TWNMb3c9PSIsInZhbHVlIjoiTkJ2YUd4c3NvZkVVUlExK0grazBWQnVBdEduOXVsYWJGSmNkcDBxTTNlQlBzTzIyUC9FbGtMRTNqYU40QitzR2tnQ2FKV0RQUVdBYlZ2cGZhK0RZbE9YeU83QkI0bXNDcWR4WXVjcHFKYXdYczBNeWtKbVlXS3ltVFlFR3VCUzUiLCJtYWMiOiIyZWY3NTdhMjdmZTEzMDY3OWNmYTYwNDA2ZjRlZDA3N2U4ODg5YzQyM2JlNDMyMWJjNGVkMzBlNjA5NzhlZmMwIiwidGFnIjoiIn0%3D; expires=Wed, 04-Jun-2025 21:03:43 GMT; path=/; httponlyaskhelpdesk_session=eyJpdiI6IkZXNFFIVTRsVVVoak5nYzZ1TWNMb3c9PSIsInZhbHVlIjoiTkJ2YUd4c3NvZkVVUlExK0grazBWQnVBdEduOXVsYWJGSmNkcDBxTTNlQlBzTzIyUC9FbGtMRTNqYU40Qitz" ] ]
        session_attributes
        0 of 0
        array:4 [ "_token" => "IIgykXGos2lbpQilvaY5x3RQnWK793lmnCCn1EAi" "_previous" => array:1 [ "url" => "https://receivinghelpdesk.com/ask/how-do-you-find-the-class-boundaries-in-a-frequency-distribution" ] "_flash" => array:2 [ "old" => [] "new" => [] ] "PHPDEBUGBAR_STACK_DATA" => [] ]