Question

Question #15f2d

Answer 1

1) `x = 7`.
2) Median = `7.5`

Explanation:

Recall that the arithmetic mean `bar x` of a data set may be determined as follows:

`bar x = sum_(i=1)^n x_i/n`. where n = number of numbers you adding up and `x`= the number

Thus, for our initial data set:

`6 = (4+5+x+8+9+3)/6 -> 36 = 29 + x -> x = 7` (6x6=36)

For our second data set:

`8 = (10 + 8 + 7 + 12 + 6 + 10 + 4 + x)/8 -> 64 = 57 + x -> x = 7` (8x8 = 64)

However, we are not looking for `x` in the second problem. We are looking for the median. Recall that the median is simply the value in the data set which separates the upper half of the data from the lower half. In this case, since we have an even number of values, our median will be the mean of the two middle numbers when the data is listed in ascending or descending numerical order.

`4, 6, 7, **7, 8**, 10, 10, 12`

Our middle values are 7 and 8. The arithmetic mean between the two would be `(7+8)/2`, or `7.5`.

Answer 2

If the mean of the numbers`4,5,x,8,9 and 3` is `6`, then `x=7`.

If the mean of `10,8,7,12,x,6,10 and 4` is `8`, then `x=7` and the median is `7.5`.

Explanation:

The mean of the numbers given is:

Mean = sum of numbers divided by the number of numbers.

Then for the first set: `6=(4+5+x+8+9+3)/6`

`36=x+29`

`x=36-29`

`x=7`

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Then for the second set:

`8=(10+8+7+12+x+6+10+4)/8`

`64=x+57`

`x=64-57`

`x=7to` now we can find the median by re-ordering the numbers:

`4, 6, 7, 7, 8, 10, 10, 12to` to find out what is in the center:

`cancel(4, 6, 7,) 7, 8, cancel(10, 10, 12)to` which leaves us with `7, 8`.

The median is now half-way between `7 and 8`, so it is `7.5`.