# MTH156 CSU Mod 2 Descriptive Statistics & Correlation Coefficient Report

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Ynfirtnfmra1

Mathematics

## Description

Instructions

Today there are 195 sovereign countries in the world that are officially recognized. One can choose to look at many types of data coming from these countries, as there is a plethora of existing information. For this assignment you will be looking at populations of cities within China at three different times (depending on when a census was taken). The data for these cities can be found in the file named (attached) Populations. Use all of the data points for each of the years given, but please note that not every city has a population for each census.

Prepare a report (see below) using numerical methods of descriptive statistics to show how the populations of the cities vary over the years (growth rates). Be sure to include the following three (3) items in your report.

• Compute descriptive statistics for each of the years along with an explanation of what the descriptive statistics tell us about the different years. Are they continually growing, or is there a decrease in the number of people? The descriptive statistics will include the mean, mode, range, standard deviation, and the 5-number summary (minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum).
• Determine which cities, if any, should be considered outliers in each of the years? If there are any outliers in any year, please list them and state for which year each one is an outlier. Use the z-score method to determine outliers for this question showing the z-score calculations for each city and year in your spreadsheet.
• Determine the correlation coefficient between the first year and each of the other years. Please provide an explanation of the relationships. Show your calculations for each correlation coefficient within the spreadsheet.

Paper Requirements

Write a report. Items that should be included, at a minimum, are a title page, an introduction, a body which answers the questions posed in the problem, and a conclusion paragraph that addresses your findings and what you have determined from the data and your analysis. As with all written assignments, you should have in-text citations and a reference page. Please include any tables of calculations, calculated values, and graphs associated with this problem in the body of your assignment response.

Note: You must submit your Excel file with your report. This will aid in grading with partial credit if errors are found in the report.

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China Cities Name Anshan Anyang Baoding Baoji Baotou Beijing Bengbu Benxi Changchun Changde Changsha (incl. Wangcheng) Changshu Changzhou (incl. Wujin) Chaozhou (incl. Chao'an) Chengdu (incl. Xindu) [Chengtu] Chifeng (Ulanhadhot) Chongqing (incl. Ba'nan, Jiangbei) [Chungking] Cixi Dalian [Dairen] Dandong Daqing Datong Dongguan Dongying Foshan (incl. Gaoming, Nanhai, Sanshui, Shunde) Fushun Fuxin Fuyang Fuzhou Guangzhou (incl. Huade, Panyu) [Canton] Guilin (incl. Lingui) Guiyang Haikou (incl. Qiongshan) Handan Hangzhou (incl. Xiaoshan, Yuhang) [Hangchou] Harbin (incl. Hulan) Hefei [Hofei] Hengyang Hohhot (Huhehaote) [Huhehot] Huai'an (Huaiyin) Native Name 鞍山市 安阳市 保定市 宝鸡市 包头市 北京市 蚌埠市 本溪市 长春市 常德市 长沙市 常熟市 常州市 潮州市 成都市 赤峰市 重庆市 慈溪市 大连市 丹东市 大庆市 大同市 东莞市 东营市 佛山市 抚顺市 阜新市 阜阳市 福州市 广州市 桂林市 贵阳市 海口市 邯郸市 杭州市 哈尔滨市 合肥市 衡阳市 呼和浩特市 淮安市 Administrative Regions LN HEN HEB SN NM BJ AH LN JL HN HN JS JS GD SC NM CQ ZJ LN LN HL SX GD SD GD LN LN AH FJ GD GX GZ HI HEB ZJ HL AH HN NM JS Huaibei Huainan Huizhou (incl. Huiyang) Jiangmen (incl. Xinhui) Jiangyin Jiaxing Jieyang (incl. Jiedong) Jilin Jinan Jingzhou (incl. Jiangling, Shashi) Jining Jinjiang Jinzhou Kunming (incl. Chenggong) Kunshan Lanzhou Lianyungang Linyi Liuzhou Luoyang Mianyang Mudanjiang Nanchang Nanchong Nanjing (incl. Jiangning, Jiangpu, Luhe) [Nanking] Nanning (incl. Yongning) Nantong (incl. Tongzhou) Nanyang Ningbo (incl. Yinzhou) Pingdingshan Puning Putian Qingdao [Tsingtao] Qingyuan (incl. Qingxin) Qinhuangdao Qiqihar Quanzhou Rizhao Rui'an Shanghai Shantou (incl. Chaoyang, Chenghai) Shenyang Shenzhen (incl. Bao'an) Shijiazhuang Shuangliu Suqian Suzhou (incl. Wujiang, Wuzhong) 淮北市 淮南市 惠州市 江门市 江阴市 嘉兴市 揭阳市 吉林市 济南市 荆州市 济宁市 晋江市 锦州市 昆明市 昆山市 兰州市 连云港市 临沂市 柳州市 洛阳市 绵阳市 牡丹江市 南昌市 南充市 南京市 南宁市 南通市 南阳市 宁波市 平顶山市 普宁市 莆田市 青岛市 清远市 秦皇岛市 齐齐哈尔市 泉州市 日照市 瑞安市 上海市 汕头市 沈阳市 深圳市 石家庄市 双流县 宿迁市 苏州市 AH AH GD GD JS ZJ GD JL SD HB SD FJ LN YN JS GS JS SD GX HEN SC HL JX SC JS GX JS HEN ZJ HEN GD FJ SD GD HEB HL FJ SD ZJ SH GD LN GD HEB SC JS JS Tai'an Taiyuan Taizhou (Jiaojiang) Tangshan (incl. Fengnan, Fengrun) Tengzhou Tianjin [Tientsin] Ürümqi (Wulumuqi) (incl. Miquan) Wanzhou (Wanxian) Weifang Wenzhou Wuhan (incl. Hanyang, Huangpi, Wuchang, Xinzhou) Wuhu Wuxi Xiamen (Amoy) Xi'an (incl. Chang'an, Lintong) [Sian] Xiangtan Xiangyang (Xiangfan) Xianyang Xining Xinxiang Xuzhou (incl. Tongshan) Yancheng Yangzhou Yantai Yichang Yinchuan Yingkou Yiwu Yueyang Zaozhuang Zhangjiagang Zhangjiakou Zhanjiang Zhengzhou Zhenjiang Zhongshan Zhuhai (incl. Doumen) Zhuzhou Zibo 泰安市 太原市 台州市 唐山市 滕州市 天津市 乌鲁木齐市 万州区 潍坊市 温州市 武汉市 芜湖市 无锡市 厦门市 西安市 湘潭市 襄阳市 咸阳市 西宁市 新乡市 徐州市 盐城市 扬州市 烟台市 宜昌市 银川市 营口市 义乌市 岳阳市 枣庄市 张家港市 张家口市 湛江市 郑州市 镇江市 中山市 珠海市 株洲市 淄博市 SD SX ZJ HEB SD TJ XJ CQ SD ZJ HB AH JS FJ SN HN HB SN QH HEN JS JS JS SD HB NX LN ZJ HN SD JS HEB GD HEN JS GD GD HN SD Population 1/Jul/1990 1,233,947 410,367 471,270 401,237 1,044,088 5,521,949 447,084 759,083 1,721,579 275,195 1,151,155 146,490 525,085 333,390 1,866,826 345,035 2,518,721 207,178 1,884,310 543,027 756,444 917,288 552,328 394,996 901,455 1,288,959 600,124 142,170 875,173 3,336,361 424,373 1,079,652 411,212 525,391 1,654,923 2,690,391 714,242 503,725 634,514 330,379 Population 1/Nov/2000 1,389,660 768,992 902,496 645,414 1,420,047 10,300,723 696,811 860,838 2,750,204 759,262 2,233,790 565,178 1,513,152 708,368 4,273,218 692,267 4,912,732 675,727 2,872,048 684,190 1,094,892 1,053,616 3,870,036 638,035 4,006,681 1,359,873 669,355 742,862 2,032,723 7,547,467 814,246 1,894,344 1,028,724 822,387 3,240,947 3,627,082 1,549,476 804,818 1,020,152 842,628 Population 1/Nov/2010 1,504,996 908,129 1,038,195 871,940 1,900,373 16,446,857 793,866 1,000,128 3,411,209 846,308 3,193,354 929,124 2,257,376 1,256,268 6,316,922 902,285 6,263,790 1,059,942 3,902,467 775,787 1,433,698 1,362,314 7,271,322 848,958 6,771,895 1,318,808 750,283 780,522 2,824,414 9,702,144 963,629 2,520,061 1,517,410 919,295 5,162,093 4,596,313 3,098,727 1,115,645 1,497,110 1,523,655 290,390 724,157 302,636 379,397 129,544 209,898 176,421 1,090,329 1,437,596 457,286 183,063 97,990 591,653 1,114,413 96,625 1,289,756 344,244 260,558 636,828 725,360 232,035 570,273 911,872 348,201 2,322,947 817,206 457,388 228,293 753,719 430,841 75,593 131,972 1,332,074 167,892 358,006 1,115,298 173,571 248,388 230,138 7,821,787 1,750,256 3,650,678 1,081,621 1,077,297 83,529 97,724 872,673 632,592 1,062,430 1,057,659 876,531 555,454 451,443 936,485 1,448,434 2,795,070 784,584 882,894 480,433 776,628 2,587,824 434,429 1,914,163 576,477 1,186,215 1,043,458 1,233,775 782,461 672,345 1,680,756 621,403 4,042,337 1,667,159 1,032,414 696,638 1,696,811 871,274 646,327 627,124 2,720,972 350,545 718,229 1,338,587 764,100 631,562 465,230 14,230,992 3,070,364 4,596,785 6,480,340 1,935,553 155,754 414,408 2,160,907 854,696 1,238,488 1,807,858 1,480,023 1,013,670 762,643 1,226,848 1,469,722 3,527,566 904,157 939,034 1,172,827 946,098 3,278,777 1,118,617 2,438,595 897,393 1,522,488 1,410,712 1,584,463 967,007 790,623 2,223,661 890,402 5,827,888 2,660,833 1,612,385 899,899 2,583,073 855,130 874,954 1,107,199 3,519,919 916,453 967,877 1,314,720 1,154,731 902,272 927,383 20,217,748 3,644,017 5,718,232 10,358,381 2,770,344 795,123 783,376 4,083,923 366,443 1,577,640 125,306 1,088,214 175,562 4,090,643 1,172,018 207,055 392,644 456,319 3,791,622 441,999 775,702 423,796 2,398,634 456,050 462,113 316,641 592,115 450,347 809,384 293,924 302,007 422,282 412,605 383,654 458,353 114,258 304,565 302,641 59,091 558,286 485,833 1,134,174 328,121 393,353 269,457 429,858 776,912 937,761 2,538,336 1,200,809 1,660,054 506,623 6,755,403 1,829,555 574,033 1,263,016 1,583,387 5,921,960 641,259 1,872,915 1,454,450 3,870,504 707,783 1,204,039 814,625 854,466 775,941 1,623,307 933,832 865,117 1,261,476 869,092 578,362 630,208 560,317 845,109 883,031 432,352 806,518 832,273 2,501,024 764,105 1,434,251 1,056,169 837,102 1,929,403 1,123,541 3,154,157 1,189,276 2,128,191 783,473 9,290,263 2,853,398 859,662 1,261,582 2,686,825 6,841,779 1,108,087 2,757,736 3,119,110 5,206,253 903,287 1,433,057 835,648 1,153,417 918,078 2,214,795 1,136,826 1,077,531 1,797,861 1,049,363 1,159,457 880,412 878,903 924,099 980,893 762,625 924,628 1,038,762 3,677,032 950,516 2,740,994 1,369,538 999,404 2,261,717
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Running head: STATISTICAL REPORT OF THE POPULATION OF CHINA'S CITIES

STATISTICAL REPORT OF THE POPULATION OF CHINA'S CITIES
Name:
Institution affiliation:
Date:

1

STATISTICAL REPORT OF THE POPULATION OF CHINA'S CITIES

2

STATISTICAL REPORT OF THE POPULATION OF CHINA'S CITIES
Introduction
Generally, the human population as kept on increasing gradually over the year. To
determine the rate of population increase, each country has its census program. In most
countries, the census is carried out at an interval of ten years. Understating the rate of population
increase is very important to the government because it facilitates proper planning. This report
comprises the results of the analysis of populations of cities within China in 1990, 2000, and
2010.
Descriptive statistics
1990

2000

2010

Descriptive statistics
Mean
Mode
Standard deviation
Minimum
Maximum
Range

844,604
#N/A
1066567.66
59,091
7,821,787
7,762,696

1,680,030
#N/A
1919368.568
155,754
14,230,992
14,075,238

2,356,762
#N/A
2790720.105
750,283
20,217,748
19,467,465

5-number summary
Minimum
1st quartile
Median
3rd quartile
Maximum

59,091
302639.75
457,871
1052390.25
7,821,787

155,754
705040
937,123
1840395
14,230,992

750,283
922898
1,247,378
2745179.5
20,217,748

The descriptive statistics above indicate that the population in many cities in China kept
on increasing from 1990 to 2010. The average population of the cities in China increased from
844,604 in 1990 to 2,356,762 in 2010. The standard deviation and the range also increased
significantly over the years (Holcomb, 2017).

STATISTICAL REPORT OF THE POPULATION OF CHINA'S CITIES

3

Outliers
The cities that should be considered outliers were determined by the z-score method in
excel spreadsheet. From the results obtained, Zhuhai, Zhuzhou, and Zibo should be considered as
outliers in 1990 and 2000. The z-scores for these cities are above 3.0. This implies that the values
for the populations of these cities deviated from the values of other populations by a large
margin. Also, Zhuzhou and Zibo can be considered outliers in 2010 because their z-scores
exceed 3.0.
Correlation coefficients
The correlation coefficient between 1990 and 2000 and 1990 and 2010 was computed
using excel function. The correlation coefficient between 1990 and 2000 is 0.9388, indicating a
strong positive correlation between the variables (Hayslett & Murphy, 2014). This implies that
the populations of the cities increased significantly in both 1990 and 2000. Also, the correlation
coefficient between 1990 and 2010 is 0.8969, indicating a strong positive correlation.
Nevertheless, the correlation coefficient between 1990 and 2000 and 1990 and 2010 can be
illustrated using a scatter plot, as shown below.

Population in 2000

Scater plot
16,000,000
14,000,000
12,000,000
10,000,000
8,000,000
6,000,000
4,000,000
2,000,000
0

y = 1.6895x + 253063
R² = 0.8814

0

2,000,000

4,000,000

6,000,000

Population in 1990

8,000,000 10,000,000

STATISTICAL REPORT OF THE POPULATION OF CHINA'S CITIES

Scatter plot
Population in 2010

25,000,000
20,000,000

y = 2.3468x + 374606
R² = 0.8045

15,000,000
10,000,000
5,000,000
0
0

2,000,000 4,000,000 6,000,000 8,000,000 10,000,000

Population in 1990

Conclusion
In summary, the populations of all the cities in China increased significantly from 1990
to 2010 as indicated by the descriptive statistics and correlation coefficients. There is a strong
positive correlation between the populations of the cities in 1990 and 2000 and 1990 and 2010.

4

STATISTICAL REPORT OF THE POPULATION OF CHINA'S CITIES
References
Hayslett, H., & Murphy, P. (2014). Statistics. London: Elsevier Science.
Holcomb, Z. (2017). Fundamentals of descriptive statistics. London: Routledge.

5

China
Cities
Name
Anshan
Anyang
Baoding
Baoji
Baotou
Beijing
Bengbu
Benxi
Changchun
Changde
Changsha (incl. Wangcheng)
Changshu
Changzhou (incl. Wujin)
Chaozhou (incl. Chao'an)
Chengdu (incl. Xindu) [Chengtu]
Chongqing (incl. Ba'nan, Jiangbei) [Chungking]
Cixi
Dalian [Dairen]
Dandong
Daqing
Datong
Dongguan
Dongying
Foshan (incl. Gaoming, Nanhai, Sanshui, Shunde)
Fushun
Fuxin
Fuyang
Fuzhou
Guilin (incl. Lingui)
Guiyang
Haikou (incl. Qiongshan)
Handan
Hangzhou (incl. Xiaoshan, Yuhang) [Hangchou]
Harbin (incl. Hulan)
Hefei [Hofei]
Hengyang
Hohhot (Huhehaote) [Huhehot]
Huai'an (Huaiyin)

Native Name

LN
HEN
HEB
SN
NM
BJ
AH
LN
JL
HN
HN
JS
JS
GD
SC
NM
CQ
ZJ
LN
LN
HL
SX
GD
SD
GD
LN
LN
AH
FJ
GD
GX
GZ
HI
HEB
ZJ
HL
AH
HN
NM
JS

Huaibei
Huainan
Huizhou (incl. Huiyang)
Jiangmen (incl. Xinhui)
Jiangyin
Jiaxing
Jieyang (incl. Jiedong)
Jilin
Jinan
Jingzhou (incl. Jiangling, Shashi)
Jining
Jinjiang
Jinzhou
Kunming (incl. Chenggong)
Kunshan
Lanzhou
Lianyungang
Linyi
Liuzhou
Luoyang
Mianyang
Mudanjiang
Nanchang
Nanchong
Nanjing (incl. Jiangning, Jiangpu, Luhe) [Nanking]
Nanning (incl. Yongning)
Nantong (incl. Tongzhou)
Nanyang
Ningbo (incl. Yinzhou)
Pingdingshan
Puning
Putian
Qingdao [Tsingtao]
Qingyuan (incl. Qingxin)
Qinhuangdao
Qiqihar
Quanzhou
Rizhao
Rui'an
Shanghai
Shantou (incl. Chaoyang, Chenghai)
Shenyang
Shenzhen (incl. Bao'an)
Shijiazhuang
Shuangliu
Suqian
Suzhou (incl. Wujiang, Wuzhong)

�...

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Anonymous
Really great stuff, couldn't ask for more.

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