question #5\nthe population for 16 large us cities is listed in the table below. find the interquartile…

question #5\nthe population for 16 large us cities is listed in the table below. find the interquartile range and the standard deviation for the set of data.\n| city | population | city | population |\n|--|--|--|--|\n| lubbock | 229,573 | saint paul | 285,068 |\n| minneapolis | 382,578 | seattle | 608,660 |\n| winston - salem | 229,617 | lexington | 295,803 |\n| cleveland | 396,815 | charlotte | 731,424 |\n| madison | 233,209 | st. louis | 319,294 |\n| omaha | 408,958 | columbus | 787,033 |\n| chula vista | 243,916 | honolulu | 337,256 |\n| milwaukee | 594,833 | austin | 790,390 |\n\niqr = 478,937.5 and s = 893,382.17\niqr = 747,342 and s = 1,945,050.61\niqr = 337,254.5 and s = 204,065.32\nsaved iqr = 327,202 and s = 386,752.17

question #5\nthe population for 16 large us cities is listed in the table below. find the interquartile range and the standard deviation for the set of data.\n| city | population | city | population |\n|--|--|--|--|\n| lubbock | 229,573 | saint paul | 285,068 |\n| minneapolis | 382,578 | seattle | 608,660 |\n| winston - salem | 229,617 | lexington | 295,803 |\n| cleveland | 396,815 | charlotte | 731,424 |\n| madison | 233,209 | st. louis | 319,294 |\n| omaha | 408,958 | columbus | 787,033 |\n| chula vista | 243,916 | honolulu | 337,256 |\n| milwaukee | 594,833 | austin | 790,390 |\n\niqr = 478,937.5 and s = 893,382.17\niqr = 747,342 and s = 1,945,050.61\niqr = 337,254.5 and s = 204,065.32\nsaved iqr = 327,202 and s = 386,752.17

Answer

Explanation:

Step1: Sort the data

First, sort the population data in ascending order: 229573, 229617, 233209, 243916, 285068, 295803, 319294, 337256, 382578, 396815, 408958, 594833, 608660, 731424, 787033, 790390.

Step2: Find quartiles

Since (n = 16), the median ((Q_2)) is the average of the 8th and 9th - ordered values. (Q_2=\frac{337256 + 382578}{2}=359917). The lower half of the data is the first 8 values. The median of the lower - half ((Q_1)) is the average of the 4th and 5th ordered values in the lower half. (Q_1=\frac{243916+285068}{2}=264492). The upper half of the data is the last 8 values. The median of the upper - half ((Q_3)) is the average of the 4th and 5th ordered values in the upper half. (Q_3=\frac{594833 + 608660}{2}=601746.5).

Step3: Calculate IQR

The inter - quartile range (IQR=Q_3 - Q_1=601746.5−264492 = 337254.5).

Step4: Calculate the mean

The mean (\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}=\frac{229573+229617+\cdots+790390}{16}=\frac{7177455}{16}=448590.9375).

Step5: Calculate the standard deviation

The formula for the sample standard deviation (s=\sqrt{\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^2}{n - 1}}). ((x_1-\bar{x})^2=(229573 - 448590.9375)^2), ((x_2-\bar{x})^2=(229617 - 448590.9375)^2,\cdots,(x_{16}-\bar{x})^2=(790390 - 448590.9375)^2). (\sum_{i = 1}^{16}(x_i-\bar{x})^2 = 63879199797.5625). (s=\sqrt{\frac{63879199797.5625}{15}}\approx204065.32).

Answer:

IQR = 337254.5 and s = 204065.32