Dylan is going fishing. The lengths, in centimeters, of nine earthworms are shown below. He just caught a tenth earthworm that is 9.5 centimeters long. What is the median of the data once the tenth earthworm is included in the data set?
3, 4, 5, 5, 6, 7, 8, 9, 10
Responses
A 6.56.5
B 9.59.5
C 66
D 6.65
To find the median of a data set, we need to arrange the numbers in order from least to greatest. With the addition of the tenth earthworm, the new data set would be:
3, 4, 5, 5, 6, 7, 8, 9, 9.5, 10
There are 10 numbers in this data set, so the median would be the average of the two middle numbers. In this case, the two middle numbers are 6 and 7. The average of these two numbers is:
(6 + 7) ÷ 2 = 6.5
Therefore, the median of the data set including the tenth earthworm is 6.5.
The answer is A. 6.5.
72, 80, 74, 68, 65, 66, 72, 74, 65, 80, 74
Michale got these scores the last time he played golf. According to the data shown, what is the mode of his scores?
Responses
A 7272
B 7474
C 7171
D 6666
E 7373
F 80
The mode is the value that appears the most frequently in the data set. In this case, we see that the number 74 appears three times, which is more than any other number. Therefore, 74 is the mode of Michale's scores.
The answer is B. 74.
Find the mean of these numbers.
12, 9, 11, 8, 9, 12, 9
To find the mean (average) of these numbers, we add them together and divide by the total number of numbers:
(12 + 9 + 11 + 8 + 9 + 12 + 9) ÷ 7 = 70 ÷ 7 = 10
Therefore, the mean of these numbers is 10.
Which question is a statistical question?
Responses
A How old is my neighbor?How old is my neighbor?
B How old is my cat?How old is my cat?
C How old am I?How old am I?
D How old are the students in my school?
D How old are the students in my school?
A statistical question is a question that can be answered by collecting and analyzing data. Option A, B, and C are not statistical questions because they cannot be answered by collecting and analyzing data. Option D is a statistical question because it can be answered by collecting data on the ages of the students in the school, and then analyzing that data to determine things like the mean, median, and mode age of the students.
72, 80, 74, 68, 65, 66, 72, 70, 65, 80, 75
Jennifer's recent golf scores are shown. What is her mean score, rounded to the nearest tenth?
Responses
To find the mean, we add up all the scores and divide by the number of scores:
(72 + 80 + 74 + 68 + 65 + 66 + 72 + 70 + 65 + 80 + 75) ÷ 11 ≈ 71.5
Rounded to the nearest tenth, Jennifer's mean score is 71.5.
The answer is 71.5.
Consider this data set:
{34, 35, 42, 18, 20, 51, 19, 47, 37, 34}
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
The mean is Response area
The median is Response area
The mode is Response area
The range is Response area
Suppose the value 26 is added to the data set.
The mean decreases by Response area.
The median decreases by Response area.
The mode is Response area.
The mean is 35.2.
To find the mean, we add up all the numbers and divide by the total number of numbers:
(34 + 35 + 42 + 18 + 20 + 51 + 19 + 47 + 37 + 34) ÷ 10 = 352 ÷ 10 = 35.2
The median is 34.5.
To find the median, we need to first put the numbers in order:
{18, 19, 20, 34, 34, 35, 37, 42, 47, 51}
The middle two numbers are 34 and 35, so we take their average:
(34 + 35) ÷ 2 = 34.5
The mode is 34.
The mode is the number that appears most frequently in the data set, and in this case, 34 appears twice while no other number appears more than once.
The range is 33.
To find the range, we subtract the lowest number from the highest number:
51 − 18 = 33
If the value 26 is added to the data set, then:
The mean decreases by 0.9.
To find the new mean, we add up all the numbers (including the new one) and divide by the total number of numbers:
(34 + 35 + 42 + 18 + 20 + 51 + 19 + 47 + 37 + 34 + 26) ÷ 11 = 378 ÷ 11 = 34.4
The old mean was 35.2, so the mean decreases by:
35.2 − 34.4 = 0.8 (rounded to one decimal place)
The median stays the same.
Although we added a new data point, 26, it does not affect the middle two numbers when put in order:
{18, 19, 20, 26, 34, 34, 35, 37, 42, 47, 51}
The middle two numbers are still 34 and 35, so the median remains at 34.5.
The mode remains the same.
The mode was originally 34, and adding the new data point 26 does not change this since no other number appears more than once.
Therefore, the mode is still 34.
Note: If 26 appeared twice in the data set, then the mode would change to 26 and there would no longer be a mode of 34.
Overall, adding the value 26 to the data set lowers the mean, but does not affect the median and mode (as long as 26 only appears once).