Consider this data set:
{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
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.
Suppose the value 26 is added to the data set.
The mean decreases by ( )
The median decreases by ( )
The mode is ( )
The range is ( )
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.
To find the mean of a data set, you need to add up all the values in the data set and then divide the sum by the total number of values.
1. To find the mean of the given data set {34, 35, 42, 18, 20, 51, 19, 47, 37, 34}, you need to add up all the values:
34 + 35 + 42 + 18 + 20 + 51 + 19 + 47 + 37 + 34 = 357
Then, divide the sum by the total number of values, which is 10 (since there are 10 values in the data set):
Mean = 357 / 10 = 35.7
Therefore, the mean of the given data set is 35.7.
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To find the median of a data set, you need to arrange the values in ascending order and find the middle value. If the data set has an even number of values, you take the average of the two middle values.
2. To find the median of the given data set {34, 35, 42, 18, 20, 51, 19, 47, 37, 34}, first arrange the values in ascending order:
18, 19, 20, 34, 34, 35, 37, 42, 47, 51
Since there are 10 values in the data set, the middle value is the 5th value, which is 34.
Therefore, the median of the given data set is 34.
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To find the range of a data set, you subtract the smallest value from the largest value.
3. To find the range of the given data set {34, 35, 42, 18, 20, 51, 19, 47, 37, 34}, first find the smallest value, which is 18, and then find the largest value, which is 51.
Range = Largest value - Smallest value = 51 - 18 = 33
Therefore, the range of the given data set is 33.
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To find the mode of a data set, you identify the value(s) that appear(s) most frequently in the data set.
4. To find the mode of the given data set {34, 35, 42, 18, 20, 51, 19, 47, 37, 34}, calculate the frequency of each value:
18 appears once
19 appears once
20 appears once
34 appears twice
35 appears once
37 appears once
42 appears once
47 appears once
51 appears once
From this, we can see that 34 appears twice, which is more than any other value. Therefore, the mode of the given data set is 34.