Question

I need an excellent math person to help me solve this please

Answer 1

5

Explanation:

The mode is the value or values that appear most frequently in a dataset.

Given dataset:

• 4, 9, 5, 13, 5, 13

For the given dataset, the mode is 5 and 13, since both these values appear twice, which is the highest frequency in the dataset.

Therefore, if a number is added to the list and there is now only one mode, the added number must be 5 or 13. (If we added "4" or "9", we would have three modes, not one!).

To determine what the new number is, we must consider the median.

We are told that the new mode is equal to the new median.

The median is the middle value of a dataset when all data values are placed in order of size.

Since there will be 7 numbers in the dataset once the new number is added, the middle value will be the 4th value (when placed in order of size). This means there will be 3 data values before and 3 data values after the median. As 13 is the maximum data value, and there are currently two in the dataset, by adding a third number "13", it will still not become the median. Therefore, the number Jazmine added must be "5".

Ordered dataset with an additional "5":

• 4, 5, 5, 5, 9, 13, 13

Therefore, 5 is the median.

Ordered dataset with an additional "5":

• 4, 5, 5, 9, 13, 13, 13

Therefore, 9 is the median.

Hence proving that the new number Jazmine adds is "5".