10 Write down a set of 5 numbers which has the following values: a mean of 5 , median of 6 and mode of 7 b mean of 5, median of 4 and mode of 8 c mean of 4 , median of 4 and mode of 4 d mean of 4.5 , median of 3 and mode of 2.5 e mean of 1 , median of 0 and mode of 5 f mean of 1 , median of $1 \frac{1}{4}$ and mode of $1 \frac{1}{4}$ 11 This data contains six houses prices in Darwin. \[ \$ 324000 \$ 289000 \$ 431000 \$ 295000 \$ 385000 \$ 1700000 \] a Which price would be considered the outlier? b If the outlier was removed from the data set, by how much would the median change? (First work out the median for each case.) c If the outlier was removed from the data set, by how much would the mean change, to the nearest dollar? (First work out the mean for each case.) 12 Explain why outliers significantly affect the mean but not the median. 13 This dot plot shows the frequency of households with $0,1,2$ or 3 pets. a How many households were surveyed? b Find the mean number of pets correct to 1 decimal place. c Find the median number of pets. d Find the mode. e Another household with 7 pets is added to the list. Does this change the median? Explain.

Step 1 ：\(\text{b: mean of 5, median of 4 and mode of 8}\)

Step 2 ：\(\text{The five integers may be arranged this way: }\underline{\ \ \ }, \ \underline{\ \ \ }, \ 4, \ 8, \ 8\)

Step 3 ：\(\text{Since the mean is 5, the sum of all five integers is 25. The numbers 4, 8, and 8 total 20, leaving 5 for the sum of the first two.}\)

Step 4 ：\(\text{They can't both be 2.5 since 8 is the only mode, so they are 1 and 4. The set is }\{1, 4, 4, 8, 8\}\)

Step 5 ：\(\text{c: mean of 4 , median of 4 and mode of 4}\)

Step 6 ：\(\text{The five integers may be arranged this way: }\underline{\ \ \ }, \ 4, \ 4, \ 4, \ \underline{\ \ \ }\)

Step 7 ：\(\text{Since the mean is 4, the sum of all five integers is 20. The numbers 4, 4, and 4 total 12, leaving 8 for the sum of the first and last integers.}\)

Step 8 ：\(\text{They can be 2 and 6, so the set is }\{2, 4, 4, 4, 6\}\)

Step 9 ：\(\text{d: mean of 4.5 , median of 3 and mode of 2.5}\)

Step 10 ：\(\text{The five integers may be arranged this way: }\underline{\ \ \ }, \ 2.5, \ 2.5, \ 3, \ \underline{\ \ \ }\)

Step 11 ：\(\text{Since the mean is 4.5, the sum of all five integers is 22.5. The numbers 2.5, 2.5, and 3 total 8, leaving 14.5 for the sum of the first and last integers.}\)

Step 12 ：\(\text{They can be 1 and 13.5, so the set is }\{1, 2.5, 2.5, 3, 13.5\}\)

Step 13 ：\(\text{f: mean of 1 , median of }1 \frac{1}{4}\text{ and mode of }1 \frac{1}{4}\)

Step 14 ：\(\text{The five integers may be arranged this way: }\underline{\ \ \ }, \ 1 \frac{1}{4}, \ 1 \frac{1}{4}, \ \underline{\ \ \ }, \ \underline{\ \ \ }\)

Step 15 ：\(\text{Since the mean is 1, the sum of all five integers is 5. The numbers }1 \frac{1}{4}\text{ and }1 \frac{1}{4}\text{ total }2 \frac{1}{2}\text{, leaving }2 \frac{1}{2}\text{ for the sum of the first, fourth, and fifth integers.}\)

Step 16 ：\(\text{They can be }\frac{1}{2}\text{, }1\text{, and }1\text{, so the set is }\{\frac{1}{2}, 1, 1 \frac{1}{4}, 1 \frac{1}{4}, 1\}\)