Petroleum pollution in oceans stimulates the growth of certain bacteria. An assessment of this growth has been made by counting the bacteria in each of
5
randomly chosen specimens of ocean water (of a fixed size). The
5
counts obtained were as follows.
42
,
70
,
53
,
66
,
54
Find the standard deviation of this sample of numbers. Round your answer to two decimal places.
To find the standard deviation of a sample of numbers, we can use the following formula:
Standard deviation = sqrt((sum((x - x̄)^2))/(n-1))
Where:
- x is each individual number in the sample
- x̄ is the mean (average) of the sample
- n is the number of observations in the sample
Given that the sample consists of the following counts: 42, 70, 53, 66, 54, we can calculate the standard deviation as follows:
1. Calculate the mean (average) of the sample:
x̄ = (42 + 70 + 53 + 66 + 54) / 5 = 57
2. Subtract the mean from each individual number in the sample, square the result, and sum these squared differences:
sum((x - x̄)^2) = (42-57)^2 + (70-57)^2 + (53-57)^2 + (66-57)^2 + (54-57)^2
= 225 + 169 + 16 + 81 + 9
= 500
3. Divide the sum of squared differences by (n-1):
500 / (5-1) = 500 / 4 = 125
4. Take the square root of the result:
sqrt(125) = 11.18 (rounded to two decimal places)
Therefore, the standard deviation of this sample of numbers is 11.18.
The following list contains the average annual total returns (in percentage points) for
8
mutual funds. The mutual funds appear in an online brokerage firm's "all-star" list.
15
,
39
,
39
,
39
,
15
,
15
,
10
,
33
(a) What is the median of this data set? If your answer is not an integer, round your answer to one decimal place.
To find the median of a data set, we need to determine the middle value. If the data set has an odd number of values, the median is the middle value. If the data set has an even number of values, the median is the average of the two middle values.
In this case, we have 8 values.
First, let's arrange the values in ascending order:
10, 15, 15, 15, 33, 39, 39, 39
Since we have an even number of values (8), we need to find the average of the two middle values.
The two middle values are 33 and 39.
Median = (33 + 39) / 2 = 36 / 2 = 18
Therefore, the median of this data set is 18.
18 is wrong
I apologize for the mistake. Let's recalculate the median correctly.
Since we have 8 values, the median is the average of the two middle values.
The two middle values are 15 and 15 (the fourth and fifth values when arranged in ascending order).
Median = (15 + 15) / 2 = 30 / 2 = 15
Therefore, the correct median of this data set is 15.
15 is also wrong
Apologies again for the mistake. Let's calculate the median correctly.
Since we have 8 values, the median is the value that falls right in the middle when the data set is arranged in ascending order.
When arranged in ascending order, the data set becomes:
10, 15, 15, 15, 33, 39, 39, 39
The middle value is the fourth value, which is 15.
Therefore, the correct median of this data set is 15.
A survey of
10
retirees was taken. Among other things, the retirees were asked to report the age at which they retired. Here are those
10
ages (in years).
74
,
71
,
68
,
65
,
55
,
56
,
61
,
59
,
65
,
74
Send data to calculator
(a) What is the mean of this data set? If your answer is not an integer, round your answer to one decimal place.
(b) What is the median of this data set? If your answer is not an integer, round your answer to one decimal place.
(c) How many modes does the data set have, and what are their values? Indicate the number of modes by clicking in the appropriate circle, and then indicate the value(s) of the mode(s), if applicable.
zero modes
one mode:
two modes:
(a) To find the mean of a data set, we add up all the values and divide by the total number of values.
For the given data set: 74, 71, 68, 65, 55, 56, 61, 59, 65, 74
Mean = (74 + 71 + 68 + 65 + 55 + 56 + 61 + 59 + 65 + 74) / 10
= 648 / 10
= 64.8
Therefore, the mean of this data set is 64.8.
(b) To find the median of a data set, we need to determine the middle value. If the data set has an odd number of values, the median is the middle value. If the data set has an even number of values, the median is the average of the two middle values.
For the given data set: 74, 71, 68, 65, 55, 56, 61, 59, 65, 74
When arranged in ascending order, the data set becomes:
55, 56, 59, 61, 65, 65, 68, 71, 74, 74
Since we have an even number of values (10), we need to find the average of the two middle values.
The two middle values are 65 and 65.
Median = (65 + 65) / 2
= 130 / 2
= 65
Therefore, the median of this data set is 65.
(c) To determine the number of modes and their values, we need to identify the value(s) that appear most frequently in the data set.
For the given data set: 74, 71, 68, 65, 55, 56, 61, 59, 65, 74
There are no values that appear more than once, so the data set has zero modes.
Therefore, the data set has zero modes.
The following list gives the number of pets for each of 8 students.
4
,
3
,
4
,
1
,
3
,
4
,
0
,
3
Send data to calculator
Find the modes of this data set.
If there is more than one mode, write them separated by commas.
If there is no mode, click on "No mode."