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Updated: Feb. 14, 2019

Note: Our next live-moderated discussion for “What’s Going On in This Graph?” will take place on Feb. 27, 2019.

1. This graph shows the relative size of military budgets by country in 2015. It originally appeared elsewhere on NYTimes.com.

After looking closely at the graph above, think about these three questions:

• What do you notice?• What do you wonder?What are you curious about that comes from what you notice in the graph?• What might be going on in this graph?Write a catchy headline that captures the graph’s main idea. If your headline makes a claim, tell us what you noticed that supports your claim.

The questions are intended to build on one another, so try to answer them in order. Start with “I notice,” then “I wonder,” and end with “The story this graph is telling is ….” and a catchy headline.

2. Next, join the conversation by clicking on the comment button and posting in the box that opens on the right. (Students 13 and older are invited to comment. Teachers of younger students are welcome to post what their students have to say, or they can have their students use this same activity on Desmos.)

3. After you have posted, read what others have said, then respond to someone else by posting a comment. Use the “Reply” button or the @ symbol to address that student directly.

On Wednesday, Feb. 13, our collaborator, the American Statistical Association, will facilitate this discussion from 9 a.m. to 2 p.m. Eastern Time to help students’ understanding go deeper. You might use their responses as models for your own.

4. On the afternoon of Thursday, Feb. 14, we will reveal more information about the graph at the bottom of this post. Students, we encourage you to post an additional comment after reading the reveal. How does the original New York Times article and the moderators’ comments help you see the graph differently? Try to incorporate the statistical terms defined in the Stat Nuggets in your response.

_________

• Read our introductory post, which includes information about using the “Notice and Wonder” teaching strategy.• Learn about how and why other teachers are using this feature, and use the 2018-19 “What’s Going On in This Graph?” calendar to plan ahead for the 25 Wednesday releases. • Go to the A.S.A. K-12 website, which includes This is Statistics, resources, professional development, student competitions, curriculum, courses and careers.

________

Updated: Feb. 14, 2019

A graph uses data in a way that tells a story that otherwise may take paragraphs to explain. We say, “A picture is worth a 1,000 words.” And, a graph may summarize 1,000,000 numbers or more. Even though you may not be familiar with military spending by country, I bet you can tell a story just from this graph.

This is an unusual graph. The “bubbles” show you the relative size of the budgets. They may seem scattered, but they are not positioned randomly. They approximate a map of the world by displaying the relative location of each country. What do you notice by continent? What do you notice about groupings of the largest bubbles? How is the graph’s story unfolding?

This graph and the chart below appeared in the New York Times article “Is America’s Military Big Enough?” There are nine other graphs in the article, including one that depicts the sizes of the major elements of the U. S. military and another with the locations of active American forces deployed outside of the contiguous United States. Go to the article and see what else you notice about military budgets by allocation of the budget, by location and over time.

Many students wondered about the U. S. budgetary priorities. Here’s a set of responses, one responding to the other, that respectfully state opposing opinions on budgetary priorities.

I notice that America spends a lot of money on its military compared to the rest of the world. I wonder why that much money has to be spent on the military while there are homeless people and people who don’t have food to eat. (Brian of CA)

@Brian, I disagree with this statement because the government should not have to bail out its citizens when it already provides one of the most stable economies in the entire world due in part to its advanced military that is able to protect all of America’s most important trade partners who the country needs to thrive and provide the opportunities for its citizens. (Er.Ab. of CA)

Here are some of the student headlines that really capture the meaning of this graph: “Military Spending, the Window to a Country’s Soul” by Gui of Rialto, Calif., “United States Military Domination — In Spending” by Andrew of Omaha, Neb., and “Billion of Dollars on Warfare. Is It Worth It?” by Sophia of Calif.

You may want to think critically about these additional questions:

• Using what you know about geography and countries’ priorities, guess which countries the largest unidentified bubbles represent. You can go to Stockholm International Peace and Research Institute visualization to check your answers by clicking on the bubbles.This graph displays the size of military budgets of various countries. But, maybe it would be more meaningful if the military budgets were scaled by current price and exchange rates, percentage of gross domestic product (GDP), population size (per capita), or government spending.

• Go to the Stockholm International Peace and Research Institute Excel spreadsheet of 172 countries for the period 1949 - 2017, the source for our graph. Select a group of countries or maybe the five largest in each list and observe the data for each. Which countries spend the most on the military when scaling:

■ By current price and exchange rates? (Tab 5)

■ By percentage of their economies (G.D.P.)? (Tab 6)

■ By per person in their country (per capita)? (Tab 7)

■ By percentage of their government spending? (Tab 8)

Based on your findings, explain which method of calculating military spending you think is best when comparing countries.

Below, in the Stat Nuggets, we define and explain mathematical terms that apply to the graph and chart. Look into the archives to see past Stat Nuggets.

Thank you for participating in “What’s Going On in This Graph?”, which is intended to help you think critically about graphs and the underlying data. Critical thinking is an essential element of statistics, the science of learning from data. Data visualizations, like these graphs, are an important part of statistics. They help us to understand and learn from data.

Keep noticing and wondering. We continue to welcome your responses.

Join us Wednesday, Feb. 27, to notice and wonder about commuter delays. The graph will be released on Thursday, Feb. 21. We look forward to your responses between 9 a.m. - 2 p.m. Eastern Time during the live online moderation.

________

Stat Nuggets for “Is America’s Military Big Enough?”

BUBBLE MAP

A bubble map is a type of graph that displays the values of three variables for each data point. One variable is the value of the data point. The other two variables are the longitude (x-axis) and latitude (y-axis) of the data point, showing each point’s geographic location. Bubble maps are a variation of a scatter plot with dots replaced by bubbles.

In the military budgets graph, the three variables are the country’s military spending and its latitude and longitude, which give its approximate map coordinates. For example, locate New Zealand and its western neighbor Australia on the bubble map. Now, note the relatively small military budget of New Zealand as compared to Australia.

RADIUS vs. AREA of a circle

The radius of a circle r is the distance from the circle’s center to any point on the circle. Its units are, for example, kilometers. The area of a circle is the product πr2, where π is an irrational number equal to approximately 3.14. The units of a circle’s area are, for example, square kilometers (or kilometers squared).

In the military budget graph, the areas of the circles represent the relative size of the countries’ military budgets. Examine the circle for Saudi Arabia, with its billion budget, and the circle for Japan, with its billion budget — about half the Saudi Arabia budget. The area of the Saudi Arabia circle is twice the area of the Japan circle, however the Saudi Arabia radius length is not twice the radius length for the Japan circle. Do you know why?

_________

The graphs for “What’s Going On in This Graph?” are selected in partnership with Sharon Hessney, a Boston mathematics teacher. Ms. Hessney wrote the “reveal” and Stat Nuggets with Erica Chauvet, a professor at Waynesburg University in Pennsylvania, and moderated online with Heather Overstreet, a mathematics teacher at Franklin County High School, Rocky Mount, Va.

B:

大乐透开奖结果查询历史数据【五】【百】【三】【十】【七】【天】【不】【断】【更】、【两】【百】【四】【十】【四】【万】【字】、【一】【千】【一】【百】【八】【十】【六】【章】，【网】【游】【之】【瘟】【疫】【法】【神】【落】【下】【帷】【幕】。 【一】【年】【半】【的】【功】【夫】？【期】【间】【经】【历】【了】【很】【多】，【也】【学】【会】【很】【多】，【为】【什】【么】【开】【书】【呢】？ 【女】【朋】【友】【决】【定】【考】【研】【的】【那】【一】【天】？【我】【写】【下】【的】【第】【一】【章】，【我】【们】【互】【相】【鼓】【励】，【互】【相】【坚】【持】，【羡】【慕】【不】？ 【呃】，【虽】【然】【最】【终】【的】【结】【果】【不】【怎】【么】【样】？【但】【也】【算】【是】【成】【功】【走】【完】【人】【生】【中】【的】【一】【段】

“【啊】【啊】【啊】【啊】【啊】【哦】【哦】……” 【弗】【利】【萨】【顽】【强】【抵】【挡】【着】【元】【气】【弹】，【拼】【尽】【全】【力】，【竟】【然】【还】【没】【有】【被】【消】【灭】。【可】【怕】【的】【力】【量】【对】【拼】，【孙】【悟】【空】【压】【着】【元】【气】【弹】【向】【前】【推】【进】，【遇】【到】【了】【莫】【大】【的】【阻】【力】。 【是】【元】【气】【弹】【的】【威】【力】【还】【不】【够】。 “【差】【了】【一】【点】！” “【还】【有】【我】。”【贝】【利】【亚】【随】【风】【落】【地】，【抬】【起】【了】【手】，“【弗】【利】【萨】，【让】【我】【送】【你】【最】【后】【一】【程】。”【硕】【大】【的】【光】【团】【从】【贝】【利】【亚】【的】

【浩】【瀚】【无】【垠】【的】【宇】【宙】，【各】【式】【的】【天】【体】【按】【照】【各】【自】【的】【轨】【迹】【运】【行】【着】，【周】【而】【复】【始】【了】【亿】【万】【年】，【而】【且】【它】【们】【还】【将】【继】【续】【这】【样】【循】【环】，【直】【至】【永】【恒】 【但】【突】【然】【的】【某】【一】【天】，【宇】【宙】【的】【某】【处】，【黑】【暗】【悄】【然】【苏】【醒】，【张】【开】【它】【漆】【黑】【的】【爪】【牙】【向】【四】【周】【蔓】【延】，【逐】【渐】【将】【周】【围】【的】【星】【域】【吞】【噬】 【而】【方】【舟】【似】【乎】【在】【看】【着】【这】【黑】【暗】，【与】【此】【同】【时】，【黑】【暗】【也】【看】【到】【了】【它】，【当】【即】【张】【开】【漆】【黑】【的】

【山】【亭】【区】【妇】【联】【积】【极】【助】【推】【乡】【村】【文】【明】【行】【动】，【引】【导】【和】【动】【员】【广】【大】【妇】【女】【同】【志】【从】【身】【边】【做】【起】，【从】【日】【常】【做】【起】，【争】【创】【示】【范】【户】，【争】【当】【文】【明】【户】。【近】【期】【各】【镇】【街】【妇】【联】【组】【织】【广】【大】【妇】【女】【和】【巾】【帼】【志】【愿】【者】【开】【展】【家】【居】【环】【境】【整】【治】，【新】【生】【活】【新】【技】【能】【培】【训】【等】【一】【系】【列】【活】【动】。【充】【分】【发】【挥】【党】【建】【引】【领】【作】【用】，【让】【妇】【女】【在】【乡】【村】【振】【兴】【和】【文】【明】【行】【动】【中】【起】【到】【积】【极】【的】【助】【推】【作】【用】。

【冉】【不】【秋】【身】【体】【如】【雨】【后】【残】【荷】，【枯】【萎】【不】【堪】，【他】【神】【思】【困】【顿】，【一】【时】【恍】【惚】，【一】【时】【割】【裂】，【眼】【前】【竟】【看】【不】【到】【倒】【地】【的】【宋】【可】【遇】，【而】【一】【幕】【幕】【划】【过】【的】，【都】【是】【他】【们】【自】【初】【见】【起】【那】【些】【相】【处】【的】【时】【光】【碎】【片】，【吉】【光】【片】【羽】【的】【一】【角】，【也】【能】【让】【此】【刻】【干】【涸】【的】【神】【思】【重】【温】【须】【臾】【的】【柔】【软】。 【他】【又】【变】【成】【一】【个】【人】【了】【吗】？ 【不】【这】【和】【以】【往】【的】【感】【觉】【并】【不】【相】【同】，【他】【甚】【至】【有】【一】【秒】【钟】大乐透开奖结果查询历史数据【花】【钿】【委】【地】【无】【人】【收】，【翠】【翘】【金】【雀】【玉】【搔】【头】。——【白】【居】【易】《【长】【恨】【歌】》 （1）【秋】【风】【踉】【跄】(【上】） 【这】【天】【是】【唐】【糖】【与】【王】【简】【成】【婚】【的】【日】【子】。 “【哎】Candy【你】【以】【前】【说】【过】【想】【去】【海】【边】【办】【婚】【礼】【的】，【没】【想】【到】【成】【了】【草】【坪】【婚】【礼】。”【陈】【念】【念】【对】【正】【在】【戴】【耳】【环】【的】【唐】【糖】【说】【道】。 “【你】【以】【前】【不】【是】【还】【说】【过】【要】【跟】【我】【一】【起】【办】【婚】【礼】，【两】【对】【一】【起】【度】【蜜】【月】【吗】？”【唐】【糖】【看】【着】

【正】【欲】【再】【次】【扑】【向】【他】【的】【一】【群】【兵】【卒】，【顿】【时】【沸】【反】【盈】【天】，【被】【那】【吼】【声】【震】【得】【就】【地】【打】【起】【滚】【来】，【有】【些】【泛】【泛】【之】【辈】，【已】【经】【被】【震】【得】【筋】【脉】【尽】【断】、【七】【窍】【流】【血】【而】【亡】！ 【天】【空】【翱】【翔】【的】【几】【只】【乌】【鸦】，【但】【听】【几】【声】【哀】【鸣】【破】【空】【而】【来】，【已】【被】【震】【得】“【潺】【潺】”【而】【落】！ 【东】【郭】【鸢】【暗】【动】【真】【力】，【努】【力】【抵】【御】【住】【那】【阵】【震】【耳】【欲】【聋】【的】【吼】【声】，【一】【边】【已】【架】【起】【长】【弓】，【狠】【狠】【地】【瞄】【准】【了】【穿】【封】【狂】【的】【心】【窝】！

【在】【直】【升】【机】【探】【照】【灯】【的】【照】【耀】【下】，【整】【个】【大】【厦】【楼】【项】【亮】【如】【白】【昼】。 【不】【过】，【虽】【然】【探】【照】【灯】【很】【亮】，【但】【是】【也】【有】【弊】【端】。 【拉】【布】【拉】【多】【等】【人】【也】【在】【大】【厦】【楼】【项】，【在】【黑】【暗】【中】【突】【然】【闪】【起】【亮】【光】，【让】【他】【们】【眼】【睛】【有】【些】【承】【受】【不】【住】。 【全】【都】【眯】【着】【眼】【睛】【往】【前】【看】【着】，【视】【线】【受】【到】【了】【很】【大】【的】【阻】【碍】。 【秦】【风】【和】【魏】【胜】【男】【躲】【在】【一】【旁】【的】【角】【落】【里】，【靠】【着】【角】【落】【里】【的】【黑】【影】，【还】【暂】【时】【可】【以】【分】

【丛】【林】【的】【沼】【泽】【很】【有】【味】【道】，【简】【单】【来】【说】，【是】【很】【臭】。 【有】【的】【沼】【泽】【很】【深】，【只】【要】【踏】【入】【其】【中】【就】【再】【也】【没】【有】【机】【会】【再】【出】【来】，【有】【的】【沼】【泽】【很】【浅】，【就】【连】【小】【腿】【都】【淹】【不】【过】【去】。 【为】【了】【安】【全】【起】【见】，【他】【们】【并】【没】【有】【直】【接】【进】【入】【到】【那】【片】【沼】【泽】【地】【中】，【而】【是】【从】【一】【旁】【绕】【开】，【值】【得】【庆】【幸】【的】【是】，【这】【片】【沼】【泽】【并】【不】【特】【别】【大】。【短】【短】【半】【天】【时】【间】，【他】【们】【便】【已】【经】【绕】【过】【沼】【泽】。 【此】【时】，【枫】【树】

【各】【位】【书】【友】，《【都】【市】【之】【至】【尊】【帝】【主】》，【到】【这】【里】【就】【暂】【时】【告】【一】【段】【落】【了】。 【结】【尾】【算】【是】【比】【较】【开】【放】，【新】【的】【征】【战】，【还】【在】【等】【着】【夏】【禹】，【新】【的】【挑】【战】，【新】【的】【世】【界】，【也】【在】【等】【着】【他】。【诸】【天】【盛】【宴】【之】【后】，【将】【会】【开】【启】【更】【加】【波】【澜】【壮】【阔】【的】【大】【时】【代】，【还】【有】【很】【多】【英】【雄】【故】【事】。 【这】【些】，【都】【可】【以】【发】【挥】【你】【们】【的】【想】【象】。【仙】【凰】【就】【不】【用】【继】【续】【写】【那】【么】【多】【了】，【精】【力】【和】【现】【实】【各】【种】【原】【因】，【这】

（责任编辑：闭绗壹）

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