Cumulative Assessment
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| Video Game Scores | |
|---|---|
| 36 | 28 |
| 48 | x |
| 42 | 57 |
| 63 | 52 |
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36 48 42 63 28 x 57 52 Note that every value occurs one time, including 63. If we set x=63 the mode of the data will become 63. 36 48 42 63 28 63 57 52 This is because now 63 will occur more often than the other values — that is, twice. Therefore, when x=63 the mode of the scores is 63.
As we can see, these values do not give us a range of 71. To fix this, we can set x to be the greatest value of the data. By doing so the range of the data will be the difference between x and 28. x-28 Now, since we want the range to be 71 we can equate the above expression to 71 and solve it for x. 71=x-28 ⇒ x=99 Therefore, when x=99 the range of the scores is 71.