Consider this data set:

Question

{34, 35, 42, 18, 20, 51, 19, 47, 37, 34}
1. find the mean
2. find the median
3. find the range
4. find the mode

Answer 1

1. Mean:
To find the mean, add up all the numbers in the data set and divide by the total number of values.
Mean = (34 + 35 + 42 + 18 + 20 + 51 + 19 + 47 + 37 + 34) / 10
Mean = 35.7

2. Median:
To find the median, first arrange the numbers in order from lowest to highest. If there are an odd number of values, the median is the middle number. If there are an even number of values, the median is the average of the two middle numbers.
Arrange the numbers in order: 18, 19, 20, 34, 34, 35, 37, 42, 47, 51
There are 10 values, so the median is the average of the fifth and sixth numbers: (34 + 35) / 2 = 34.5

3. Range:
To find the range, subtract the smallest value from the largest value.
Range = 51 - 18
Range = 33

4. Mode:
The mode is the value that appears most often in the data set.
The value 34 appears twice, so it is the mode.

Answer 2

Suppose the value 26 is added to the data set.

The mean decreases by ( )
The median decreases by ( )
The mode is ( )
The range is ( )

Answer 3

The updated data set with the value 26 added is:

{34, 35, 42, 18, 20, 51, 19, 47, 37, 34, 26}

To find the answers to the question:

1. Mean:
The new sum of the data set is: 34 + 35 + 42 + 18 + 20 + 51 + 19 + 47 + 37 + 34 + 26 = 363
The new mean is: 363 / 11 = 33
Therefore, the mean decreases by 2 (35.7 - 33 = 2).

2. Median:
The median is still the average of the fifth and sixth values since 26 is the second smallest number in the data set.
The median is: (34 + 35) / 2 = 34.5
Therefore, the median decreases by 0 (34.5 - 34.5 = 0).

3. Mode:
The mode is still 34 since it is still the number that appears most frequently.

4. Range:
The range is calculated by subtracting the smallest value (18) from the largest value (51).
The range is: 51 - 18 = 33
Therefore, the range remains the same.