Question

1. a set of test scores has the following 5 - number summary: minimum q1 median q3 maximum 2 18 22.5 28.5 33 which statement about outliers must be true? (a) there is exactly one outlier on the lower end. (b) there is at least one outlier on the lower end. (c) there is exactly one outlier on the higher end. (d) there is at least one outlier on the higher end. (e) there are no outliers. 3) home prices in a neighborhood vary every year. in 2021, the following ten home prices were listed (in thousands): h 120 166 173 h h h 123 127 l where l indicates a home below $110 and h indicates a home above $190. the median home price is (a) 166 (b) 169.5 (c) 170 (d) 173 (e) cannot be determined 4) mrs. g took her daughter, susie, to the pediatrician for her 1 - year check - up. the doctor said she was at the 95th percentile for her height. which of the following is the correct interpretation of percentile? (a) susies height is 95% above the mean height for all babies. (b) susies height is 95% below the mean height for all babies. (c) susies height is less than 95% of all baby heights. (d) susies height is more than 95% of all baby heights. (e) the distance between susies height and the mean height for all babies is 95.

Explanation:

2)

Step1: Calculate the inter - quartile range (IQR)

IQR = Q3 - Q1. Given Q1 = 18 and Q3 = 28.5, so IQR=28.5 - 18=10.5.

Step2: Calculate the lower fence

Lower fence = Q1−1.5×IQR. Substitute the values: Lower fence = 18−1.5×10.5=18 - 15.75 = 2.25. The minimum value is 2, which is less than 2.25. So there is at least one outlier on the lower end.

Step3: Calculate the upper fence

Upper fence = Q3 + 1.5×IQR. Substitute the values: Upper fence=28.5+1.5×10.5=28.5 + 15.75=44.25. The maximum value is 33, which is less than 44.25, so there are no outliers on the higher end.

There are 10 data - points. The median of 10 data - points is the average of the 5th and 6th ordered data - points. Since we have 3 H's (values above 190), 1 value of 173, 1 value of 166, 1 value of 127, 1 value of 123, and 1 L (value below 110), when we order the data, the 5th and 6th values are 166 and 173. The median is $\frac{166 + 173}{2}=169.5$.

The pth percentile of a data set is a value such that p percent of the data values are less than or equal to that value. If Susie is at the 95th percentile for her height, it means that her height is greater than 95% of all baby heights.

Answer:

B. There is at least one outlier on the lower end.

3)