Find the mean, median, and mode for the data set.
15, 16, 21, 23, 25, 25, 25, 39
Mean: To find the mean, add up all the numbers and divide by the total number of numbers.
15 + 16 + 21 + 23 + 25 + 25 + 25 + 39 = 189
189 ÷ 8 = 23.625
The mean is 23.625.
Median: To find the median, list the numbers in order from least to greatest and find the middle number.
15, 16, 21, 23, 25, 25, 25, 39
The middle number is 25, so the median is 25.
Mode: To find the mode, look for the number that appears most frequently.
15, 16, 21, 23, 25, 25, 25, 39
The number 25 appears 3 times, which is more than any other number, so the mode is 25.
In the following list of data, find the range:
21, 28, 31, 35, 39, 43, 51, 60.
The range is the difference between the highest value and the lowest value.
Highest value: 60
Lowest value: 21
Range = Highest value - Lowest value
Range = 60 - 21
Range = 39
The range is 39.
Pat recorded the weights of the first 10 fish she caught and released at Mirror Lake this season.
The weights were 8 lb, 6 lb, 9 lb, 6 lb, 7 lb, 5 lb, 7 lb, 6 lb, 23 lb, and 6 lb.
What is the median of the data set?
To find the median, we need to first put the weights in order from least to greatest:
5 lb, 6 lb, 6 lb, 6 lb, 7 lb, 7 lb, 8 lb, 9 lb, 23 lb
There are 10 weights in total, which means the middle weight(s) will be the 5th and 6th weights.
Median = (6 lb + 7 lb) / 2
Median = 6.5 lb
Therefore, the median weight of Pat's 10 fish is 6.5 pounds.
Identify the outlier for the following data set:
2.4, 5.3, 3.5, 22.6, 1.8, 2.1, 4.6.
To identify the outlier for this data set, we can use a rule of thumb that an outlier is any data point that is more than 1.5 times the interquartile range (IQR) below the first quartile (Q1), or above the third quartile (Q3).
First, let's find the quartiles of the data set:
- Put the data in order from least to greatest: 1.8, 2.1, 2.4, 3.5, 4.6, 5.3, 22.6
- Find the median (Q2) of the entire data set: Q2 = 3.5
- Find the median (Q1) of the lower half of the data set (1.8, 2.1, 2.4, 3.5): Q1 = 2.1
- Find the median (Q3) of the upper half of the data set (4.6, 5.3, 22.6): Q3 = 5.3
Next, let's calculate the IQR:
IQR = Q3 - Q1 = 5.3 - 2.1 = 3.2
According to the rule of thumb, any data point that is more than 1.5 times the IQR below Q1 or above Q3 is an outlier.
Lower threshold for outliers: Q1 - 1.5(IQR) = 2.1 - 1.5(3.2) = -2.3
Upper threshold for outliers: Q3 + 1.5(IQR) = 5.3 + 1.5(3.2) = 9.7
The data point 22.6 is above the upper threshold of 9.7, so it is considered an outlier in this data set.
Therefore, the outlier for this data set is 22.6.