Statistics and Descriptive Data
Analyzing data with mean, median, mode, range, and displays
Statistics and Descriptive Data
Analyzing data with mean, median, mode, range, and displays
Math - Grade 6-8
- 1
Find the mean of this data set: 6, 8, 10, 12, 14.
Mean is the average.
The mean is 10. Add the numbers to get 50, then divide by 5 because there are 5 values. - 2
Find the median of this data set: 3, 7, 9, 11, 15.
The median is 9. When the numbers are in order, the median is the middle value. - 3
Find the mode of this data set: 4, 6, 6, 8, 9, 9, 9, 10.
Mode means the value that occurs most often.
The mode is 9. It appears more often than any other number in the data set. - 4
Find the range of this data set: 18, 22, 25, 19, 30, 24.
The range is 12. Subtract the smallest value, 18, from the largest value, 30. - 5
Find the mean, median, mode, and range of this data set: 5, 7, 7, 8, 10, 13.
Work one statistic at a time.
The mean is about 8.3, the median is 7.5, the mode is 7, and the range is 8. The sum is 50, and 50 divided by 6 is about 8.3. The middle two numbers are 7 and 8, so the median is 7.5. The greatest value is 13 and the least value is 5. - 6
A student recorded the number of books read by 7 classmates: 2, 4, 4, 5, 6, 8, 11. Which measure of center, mean or median, better describes this data set, and why?
The median better describes this data set because the value 11 is higher than the rest and pulls the mean upward. The median is less affected by an unusually large value. - 7
The temperatures for five days were 70, 72, 68, 74, and 71 degrees. Find the mean temperature.
Add all five temperatures first.
The mean temperature is 71 degrees. The sum is 355, and 355 divided by 5 equals 71. - 8
This data set shows the number of goals scored in 8 games: 1, 3, 2, 4, 2, 5, 2, 3. Find the median and mode.
The median is 2.5 and the mode is 2. In order, the data are 1, 2, 2, 2, 3, 3, 4, 5. The middle two values are 2 and 3, so the median is 2.5. - 9
A line plot shows test scores of 72, 75, 75, 80, 84, 84, 84, and 90. Find the mode and range.
Look for the most frequent score and the difference between the highest and lowest scores.
The mode is 84 and the range is 18. The value 84 appears most often, and 90 minus 72 equals 18. - 10
A data set has a mean of 12 for 4 numbers. What is the total of the 4 numbers?
The total is 48. Multiply the mean, 12, by the number of values, 4. - 11
A data set is 9, 12, 15, 18, 21. If each value increases by 3, what happens to the mean and median?
Think about how adding the same number to every data value changes the set.
Both the mean and the median increase by 3. Adding the same amount to every value shifts the center of the data by that amount. - 12
The table below shows the number of pets owned by students: 0, 1, 1, 2, 2, 2, 3, 5. Which is greater, the mean or the median?
The mean is greater than the median. The median is 2, and the mean is 16 divided by 8, which is also 2, so in this case they are equal, not greater. Both measures are 2. - 13
A class collected the following data for minutes spent reading: 10, 15, 20, 20, 25, 30, 30, 30, 35. Describe the distribution using center and spread.
Use at least one measure of center and one measure of spread.
The data are centered around 20 to 30 minutes. The median is 25, the mode is 30, and the range is 25 because 35 minus 10 equals 25. This means most students read for about 25 to 30 minutes, with a spread from 10 to 35 minutes. - 14
A student says that the mode is always the best measure of center. Is the student correct? Explain.
The student is not correct. The mode can be useful, but it is not always the best measure of center because some data sets have no mode, more than one mode, or a mode that does not represent the overall data well. - 15
The data set 14, 16, 18, 20, 22 has one more value added, and the new mean is 19. What number was added?
Use mean times number of values to find the new total.
The number added was 24. The original total is 90. With 6 numbers and a mean of 19, the new total must be 114. Then 114 minus 90 equals 24.