How To Calculate The Mean and Mode of Ungrouped Set of Data

Samples

Find the mean and the mode of the following set of data
1.) 2,3,5,7,9,9,10,11,14,and 18
2.) 3,5,8,10,12,15,and 16
3.) 2,3,4,4, 5,5,7,7,7,and 9

Solution

1. Data set: 2, 3, 5, 7, 9, 9, 10, 11, 14, 18
Mean = (2 + 3 + 5 + 7 + 9 + 9 + 10 + 11 + 14 + 18) / 10 = 8.8
Mode = 9 (because it appears most frequently, twice)

2. Data set: 3, 5, 8, 10, 12, 15, 16
Mean = (3 + 5 + 8 + 10 + 12 + 15 + 16) / 7 = 9.857 (rounded to 3 decimal places)
Mode = No mode (all values occur only once)

3. Data set: 2, 3, 4, 4, 5, 5, 7, 7, 7, 9
Mean = (2 + 3 + 4 + 4 + 5 + 5 + 7 + 7 + 7 + 9) / 10 = 5.3
Mode = 7 (because it appears most frequently, three times)

So, the mean and mode for each set of data are as follows:

1. Mean: 8.8, Mode: 9
2. Mean: 9.857, Mode: No mode
3. Mean: 5.3, Mode: 7

[mediator_tech]

1. The __________ is calculated by summing up all the values in a dataset and dividing by the total number of values.
a) Median
b) Mode
c) Mean

2. In a dataset, the __________ is the value that appears most frequently.
a) Mean
b) Median
c) Mode

3. The average of a set of values is also known as the __________.
a) Mode
b) Median
c) Mean

4. To find the mode, you look for the __________ that occurs most often in a dataset.
a) Highest value
b) Lowest value
c) Value

5. If there are two values that appear most frequently in a dataset, it is called a __________.
a) Bimodal distribution
b) Unimodal distribution
c) Trimodal distribution

6. When calculating the mean, you __________ all the values and then divide by the total number of values.
a) Add
b) Multiply
c) Subtract

7. The __________ is not affected by outliers as much as the mean.
a) Mode
b) Median
c) Mean

8. If all values in a dataset are the same, the mode and mean will be __________.
a) Zero
b) Equal
c) Different

9. The measure of central tendency that’s best used for skewed data is the __________.
a) Mean
b) Median
c) Mode

10. The __________ is the value that separates the higher half from the lower half of a dataset.
a) Mode
b) Median
c) Mean

11. In a dataset, if there is no value that appears more than once, there is __________.
a) No mode
b) Only one mode
c) Multiple modes

12. The mode of a dataset is the value that occurs with the __________ frequency.
a) Highest
b) Lowest
c) Same

13. The mean can be affected by __________ values in a dataset.
a) Outliers
b) Modes
c) Medians

14. For a dataset with an even number of values, the median is the __________ of the two middle values.
a) Sum
b) Average
c) Difference

15. The __________ is the measure of how much the values in a dataset deviate from the mean.
a) Mode
b) Median
c) Standard Deviation

[mediator_tech]

Define the following 1. Mean 2. Median 3. Mode 4. Standard Deviation