Question

Challenge. Add a number to the original data set based on the instructions below:

Original data set:
3, 10, 8, 3, 10, 1, 10,
A)
Fill in the blank with a number that would make the range of the data set 20.
3, 10, 8, 3, 10, 1, 10,
B)
Fill in the blank with a number that would make the mean of the data set 15.
3, 10, 8, 3, 10, 1, 10,
C)
Fill in the blank with a number that would make the standard deviation smaller.
3, 10, 8, 3, 10, 1, 10,

Answer 1

A) 23

B) 75

C) 6.30

Explanation:

A) Range = highest value - least value

Range = 20

least value = 3

Thus,

20 = highest value - 3

highest value = 20 + 3

= 23

The number that would make the range of the data set 20 is 23.

B) Let the number be represented by x, so that;

15 =
`(3 + 10 + 8 + 3 + 10 + 1 + 10 + x)/(8)`

cross multiply to have

15 x 8 = 45 + x

120 - 45 = x

x = 75

The number that would make the mean of the data set 15 is 75.

C) The given data plus a number that is close to the mean would reduce the standard deviation.

mean of the data set =
`(3+10+8+3+10+1+10)/(7)`

= 6.43

The required number could be 6.30