{"id":9736,"date":"2015-04-12T16:36:24","date_gmt":"2015-04-12T16:36:24","guid":{"rendered":"http:\/\/www.oracletutoring.ca\/blog\/?p=9736"},"modified":"2015-04-12T16:36:24","modified_gmt":"2015-04-12T16:36:24","slug":"statistics-standard-deviation-shortcut-using-frequencies","status":"publish","type":"post","link":"https:\/\/www.oracletutoring.ca\/blog\/statistics-standard-deviation-shortcut-using-frequencies\/","title":{"rendered":"Statistics: standard deviation shortcut using frequencies"},"content":{"rendered":"

The tutor shows a convenient way to estimate the standard deviation.<\/h1>\n

Let’s imagine the following list of 20 test scores:<\/p>\n

43, 44, 49, 51, 52, 55, 57, 58, 61, 64, 68, 73, 74, 76, 77, 82, 84, 85, 87, 91<\/p>\n

Of course, you could easily get the standard deviation, mean, etc from a calculator (see my statistics<\/a> category). However, there is a shortcut method that involves dividing the numbers into ranges, then using frequencies:<\/p>\n

Step 1: Write the numbers in ascending order. (The list above is already that way.)<\/p>\n

Step 2: Organize the numbers into separate ranges – I usually use four or five:<\/p>\n\n\n\n\n\n\n\n
range<\/td>\nmidpoint<\/td>\nentries<\/td>\nfrequency<\/td>\n<\/tr>\n
43-52<\/td>\n47.5<\/td>\n43, 44, 49, 51, 52<\/td>\n5<\/td>\n<\/tr>\n
53-62<\/td>\n57.5<\/td>\n55, 57, 58, 61<\/td>\n4<\/td>\n<\/tr>\n
63-72<\/td>\n67.5<\/td>\n64, 68<\/td>\n2<\/td>\n<\/tr>\n
73-82<\/td>\n77.5<\/td>\n73, 74, 76, 77, 82<\/td>\n5<\/td>\n<\/tr>\n
83-92<\/td>\n87.5<\/td>\n84, 85, 87, 91<\/td>\n4<\/td>\n<\/tr>\n<\/table>\n

Step 3: Now, find the standard deviation as if the list consists of each range midpoint, represented by its frequency. The above list becomes<\/p>\n

47.5 (freq: 5), 57.5 (freq: 4), 67.5 (freq: 2), 77.5 (freq: 5), 87.5 (freq: 4)<\/p>\n

Each calculator I’m familiar with has a shortcut way to enter frequencies. Today, we’ll cover the Casio fx-260Solar<\/em> (see my post here<\/a> for more detail):<\/p>\n

Step 1: Press mode<\/span> then .<\/span> (decimal point) to get into SD mode.<\/p>\n

Step 2: To enter 47.5 five times, key in 47.5 X 5<\/span>, then press the M+<\/span> key.<\/p>\n

Step 3: Continue by keying 57.5 X 4 <\/span>M+<\/span> and so on.<\/p>\n

Step 4: Once you’ve worked through the list, press shift<\/span> then 6<\/span>. You should recieve the answer 20<\/span>, meaning you have entered 20 data values.<\/p>\n

Step 5: Press shift<\/span> 8<\/span> for \u03c3<\/span>n<\/sub> or shift<\/span> 9<\/span> for \u03c3<\/span>n-1<\/sub>, whichever standard deviation is desired.<\/p>\n

From my experience, \u03c3<\/span>n<\/sub> is preferred in high school, while \u03c3<\/span>n-1<\/sub> is more often used at post-secondary level. If you’re not sure which to use, ask your instructor.<\/p>\n

Here are the answers you hopefully receive. Note also the standard deviation without the shortcut:<\/p>\n\n\n\n\n\n
\u03c3<\/span>n<\/sub><\/td>\n14.99<\/span><\/td>\n<\/tr>\n
\u03c3<\/span>n-1<\/sub><\/td>\n15.38<\/span><\/td>\n<\/tr>\n
\u03c3<\/span>n<\/sub> (no shortcut)<\/td>\n14.76<\/span><\/td>\n<\/tr>\n
\u03c3<\/span>n-1<\/sub> (no shortcut)<\/td>\n15.14<\/span><\/td>\n<\/tr>\n<\/table>\n

You can see how close the shortcut values are to the real values.<\/p>\n

Note: to get out of SD mode, press mode<\/span> 0<\/span><\/p>\n

Even greater advantage from the frequency method can be realized when calculating standard deviation by hand. I’ll be talking more about that in a future post.<\/p>\n

HTH:)<\/p>\n

Source:<\/p>\n

Casio fx-260Solar User’s Guide<\/p>\n

Jack of Oracle Tutoring by Jack and Diane,<\/a> Campbell River, BC.<\/p>\n","protected":false},"excerpt":{"rendered":"

The tutor shows a convenient way to estimate the standard deviation. Let’s imagine the following list of 20 test scores: 43, 44, 49, 51, 52, 55, 57, 58, 61, 64, 68, 73, 74, 76, 77, 82, 84, 85, 87, 91 …<\/p>\n

Statistics: standard deviation shortcut using frequencies<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3,19],"tags":[91,20,695,694],"class_list":["post-9736","post","type-post","status-publish","format-standard","hentry","category-math","category-statistics","tag-casio-fx-260solar","tag-standard-deviation","tag-standard-deviation-frequency-shortcut","tag-standard-deviation-with-frequencies"],"_links":{"self":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/9736","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/comments?post=9736"}],"version-history":[{"count":36,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/9736\/revisions"}],"predecessor-version":[{"id":9772,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/9736\/revisions\/9772"}],"wp:attachment":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/media?parent=9736"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/categories?post=9736"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/tags?post=9736"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}