question #8\nfind the interquartile range and sample standard deviation for the set of data.\nsingle family…

question #8\nfind the interquartile range and sample standard deviation for the set of data.\nsingle family home prices\n339,400 345,000 332,600 341,500\n325,200 318,500 358,000 321,100\n323,700 333,800 351,000 337,700\n355,100 339,400 352,000 341,500\n337,700\n\no iqr = 18,300 and s = 12,299.9\no iqr = 11,000 and s = 8,850.79\no iqr = 22,900 and s = 12,466.55\no iqr = 19,100 and s = 11,760.5

question #8\nfind the interquartile range and sample standard deviation for the set of data.\nsingle family home prices\n339,400 345,000 332,600 341,500\n325,200 318,500 358,000 321,100\n323,700 333,800 351,000 337,700\n355,100 339,400 352,000 341,500\n337,700\n\no iqr = 18,300 and s = 12,299.9\no iqr = 11,000 and s = 8,850.79\no iqr = 22,900 and s = 12,466.55\no iqr = 19,100 and s = 11,760.5

Answer

Explanation:

Step1: Sort the data

First, sort the single - family home prices data in ascending order: 318500, 321100, 323700, 325200, 332600, 333800, 337700, 337700, 339400, 339400, 341500, 341500, 345000, 351000, 352000, 355100, 358000.

Step2: Find quartiles

There are (n = 17) data points. The median ((Q_2)) is the 9th value, so (Q_2=339400). The lower half of the data has 8 values. The median of the lower half ((Q_1)) is the average of the 4th and 5th ordered values. (Q_1=\frac{325200 + 332600}{2}=328900). The upper half of the data also has 8 values. The median of the upper half ((Q_3)) is the average of the 13th and 14th ordered values. (Q_3=\frac{345000+351000}{2}=348000).

Step3: Calculate IQR

The inter - quartile range (IQR = Q_3 - Q_1=348000 - 328900 = 19100).

Step4: Calculate sample mean

The sample mean (\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}). (\sum_{i=1}^{17}x_i=318500+321100+323700+325200+332600+333800+337700+337700+339400+339400+341500+341500+345000+351000+352000+355100+358000 = 5773500). (\bar{x}=\frac{5773500}{17}\approx339617.65).

Step5: Calculate sample standard deviation

The sample standard deviation formula is (s=\sqrt{\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^2}{n - 1}}). ((x_1-\bar{x})^2=(318500 - 339617.65)^2), ((x_2-\bar{x})^2=(321100 - 339617.65)^2), etc. After calculating (\sum_{i = 1}^{n}(x_i-\bar{x})^2) and dividing by (n - 1=16) and taking the square - root, we get (s\approx11760.5).

Answer:

IQR = 19100 and s = 11760.5