Answer:
Step-by-step explanation:
<u>Given the data set of 15 where:</u>
- Mean = 7
- Median = 6
- Mode = 5
- The minimum is 1 and the maximum is 10
<u>As per given we conclude</u>
- The set will have 7 numbers before 6 and 7 numbers after
- Sum of 15 numbers is 15*7 = 105
- The most used number is 5
a) <u>Possible set is:</u>
- 1, 5, 5, 5, 5, 5, 5, 6, 9, 9, 10, 10, 10, 10, 10
b) <u>Add number 20, the set will be:</u>
- 1, 5, 5, 5, 5, 5, 5, 6, 9, 9, 10, 10, 10, 10, 10, 20
<u>The mean is different as we have now more numbers with different sum:</u>
- (105 + 20)/(15 + 1) = 125/16 = 7.8125
<u>The median is different now and moves to the right as 20 added to the far right:</u>
<u>The mode stays same as still most used number is 5:</u>