Tia, Bill, Kay, and Marco counted the number of fireflies they saw each day for a week in the summer. They each put their numbers in order from least to greatest.
Tia: 9, 12, 15, 18, 21, 24, 27
Bill: 3, 6, 8, 18, 20, 21, 22
Kay: 14, 15, 16, 18, 24, 27, 32
Marco: 2, 6, 10, 14, 18, 22, 26
Whose data is skewed left?
A.
Tia's data
B.
Bill's data
C.
Kay's data
D.
Marco's data
To determine whose data is skewed left, we need to examine the distribution of the data.
Skewed left means that the tail of the distribution is longer on the left side. In other words, the data is concentrated towards the right and there are a few unusually low values.
Looking at the data, we can see that Tia's data is distributed evenly and does not have a longer tail on the left side.
Bill's data also does not have a longer tail on the left side; the values are distributed evenly with no unusually low values.
Kay's data is also evenly distributed without any unusually low values.
Marco's data, however, has a longer tail on the left side. The values are more concentrated towards the higher end with a few unusually low values (2 and 6).
Therefore, the answer is:
D. Marco's data
To determine which person's data is skewed left, we need to understand what it means for data to be skewed left.
Skewness is a measure of the asymmetry of a distribution. A left-skewed (or negatively skewed) distribution has a tail on the left side, meaning that the majority of data points are located towards the right side, and there are few data points towards the left side.
In this case, we can visually examine the data sets to see which one fits this description.
Tia's data: 9, 12, 15, 18, 21, 24, 27
Bill's data: 3, 6, 8, 18, 20, 21, 22
Kay's data: 14, 15, 16, 18, 24, 27, 32
Marco's data: 2, 6, 10, 14, 18, 22, 26
Looking at the numbers, we can see that Tia's data is steadily increasing and has an equal number of data points on both sides of the middle values. This means it is not skewed left.
Bill's data seems to have a fairly symmetrical distribution with most of the data points clustered towards the middle values and a few outliers towards the higher end. This is not a left-skewed distribution.
Kay's data also appears to have a fairly symmetrical distribution, with the majority of data points centered around the middle values. Like Bill's data, this is not a left-skewed distribution.
Marco's data shows a steady increase from the lower to the higher values, with very few lower values. This indicates a left-skewed distribution, with most of the values concentrated on the higher end.
Therefore, the correct answer is D. Marco's data is skewed left.
To determine whose data is skewed left, we need to compare the distribution of the numbers. In a left-skewed distribution, the majority of the numbers are on the higher end, with a tail stretching towards the lower end.
Let's compare the distributions of the data:
Tia: 9, 12, 15, 18, 21, 24, 27
Bill: 3, 6, 8, 18, 20, 21, 22
Kay: 14, 15, 16, 18, 24, 27, 32
Marco: 2, 6, 10, 14, 18, 22, 26
By looking at the data, we can see that Tia and Kay have numbers spread out relatively evenly, without a clear skew. Bill's data has a few lower numbers but is mostly spread out, so it doesn't have a clear skew either.
However, Marco's data has the majority of numbers on the lower end, with a tail stretching towards the higher end. Therefore, the data that is skewed left is Marco's data.
So, the correct answer is D. Marco's data.
The numbers of participants in various library programs are shown below.
45, 34, 49, 63, 31, 30, 46, 53, 46, 51, 61, 33, 62, 40
Which histogram represents the data correctly?
A.
The histogram has a bar between 30 and 40 is raised to 5, a bar between 40 and 50 is raised to 4, a bar between 50 and 60 is raised to 3, and a bar between 60 and 70 is raised to 2.
B.
The histogram has a bar between 30 and 40 is raised to 4, a bar between 40 and 50 is raised to 5, a bar between 50 and 60 is raised to 2, and a bar between 60 and 70 is raised to 3.
C.
The histogram has a bar between 30 and 40 is raised to 2, a bar between 40 and 50 is raised to 4, a bar between 50 and 60 is raised to 5, and a bar between 60 and 70 is raised to 3.
D.
The histogram has a bar between 30 and 40 is raised to 2, a bar between 40 and 50 is raised to 3, a bar between 50 and 60 is raised to 4, and a bar between 60 and 70 is raised to 5.
To determine which histogram represents the data correctly, we need to compare the values in the data to the heights of the bars in each histogram.
The data set is: 45, 34, 49, 63, 31, 30, 46, 53, 46, 51, 61, 33, 62, 40
Let's look at each histogram:
A) The histogram has a bar between 30 and 40 raised to 5, a bar between 40 and 50 raised to 4, a bar between 50 and 60 raised to 3, and a bar between 60 and 70 raised to 2.
B) The histogram has a bar between 30 and 40 raised to 4, a bar between 40 and 50 raised to 5, a bar between 50 and 60 raised to 2, and a bar between 60 and 70 raised to 3.
C) The histogram has a bar between 30 and 40 raised to 2, a bar between 40 and 50 raised to 4, a bar between 50 and 60 raised to 5, and a bar between 60 and 70 raised to 3.
D) The histogram has a bar between 30 and 40 raised to 2, a bar between 40 and 50 raised to 3, a bar between 50 and 60 raised to 4, and a bar between 60 and 70 raised to 5.
To decide which histogram is correct, we need to compare the heights of the bars to the frequencies of the data in each range. The frequency of a range is the number of data points falling within that range.
Counting the data points falling within each range, we find:
30-40: 3
40-50: 4
50-60: 4
60-70: 3
Comparing these frequencies to the histograms shows that the correct histogram is:
C) The histogram has a bar between 30 and 40 raised to 2, a bar between 40 and 50 raised to 4, a bar between 50 and 60 raised to 5, and a bar between 60 and 70 raised to 3.
Therefore, the correct answer is C.
Sean counted the number of stuffed animals available for prizes in each of the booths at a county fair. The list shows the results.
2, 23, 27, 29, 30, 32, 32, 34, 35, 96
Select all the data values that are outliers.
A.
2
B.
27
C.
34
D.
96
To determine if any data values are outliers, we first need to calculate the median and the interquartile range (IQR) for the given data set.
The data set is: 2, 23, 27, 29, 30, 32, 32, 34, 35, 96.
Step 1: Calculate the median
Arranging the data in order, we have: 2, 23, 27, 29, 30, 32, 32, 34, 35, 96.
The median is the middle value, which is 30.
Step 2: Calculate the IQR
The IQR is a measure of the spread or variability of the data set. It is the difference between the first quartile (Q1) and the third quartile (Q3).
To calculate the IQR, we need to find Q1 and Q3.
Q1: The median of the lower half of the data set
The lower half of the data set is: 2, 23, 27, 29, 30.
The median of the lower half is (27+29)/2 = 28.
Q3: The median of the upper half of the data set
The upper half of the data set is: 32, 32, 34, 35, 96.
The median of the upper half is (32+34)/2 = 33.
The IQR is Q3 - Q1 = 33 - 28 = 5.
Step 3: Determine outliers
An outlier is defined as a data point that is more than 1.5 times the IQR above the third quartile (Q3) or below the first quartile (Q1).
Using this definition, we can determine if any of the given data values are outliers.
For the data set: 2, 23, 27, 29, 30, 32, 32, 34, 35, 96
- The data value 2 is less than Q1 - 1.5 * IQR = 28 - 1.5 * 5 = 28 - 7.5 = 20.5. Therefore, 2 is an outlier.
- The data value 27 is not an outlier.
- The data value 34 is not an outlier.
- The data value 96 is greater than Q3 + 1.5 * IQR = 33 + 1.5 * 5 = 33 + 7.5 = 40.5. Therefore, 96 is an outlier.
So, the data values that are outliers are:
A. 2
D. 96
The dot plot below shows the number of hours that several sixth graders spent inside the school building in a day. Each X represents one student.
A dot plot showing hours from 0 to 8 in the increments of 1 has one X at 0, 2 X's at 7 and seven X's at 8.
Which of the following statements is true regarding this data? Select all that apply.
A.
The median better represents these data than the mean.
B.
The mean is affected by the one student who was absent from school.
C.
The distribution is skewed since most students were in the school building for 7 or 8 hours.
To determine which statements are true regarding this data, let's analyze the given information.
The dot plot shows the number of hours that several sixth graders spent inside the school building in a day. It represents hours from 0 to 8 with increments of 1.
Given information:
- There is one X at 0.
- There are 2 X's at 7.
- There are seven X's at 8.
Statement A: The median better represents these data than the mean.
To evaluate this statement, we need to consider the shape and distribution of the data. The median represents the middle value in a data set and is less affected by extreme values or outliers.
In this case, there are two outliers represented by the X's at 0 and 7. The majority of the students, however, spent 7 or 8 hours inside the school building. As a result, the data is skewed to the right, with a longer tail on the right side.
Since the mean is influenced by extreme values and is not appropriate for skewed data, the median would be a better representation of the central tendency in this case. Therefore, statement A is true.
Statement B: The mean is affected by the one student who was absent from school.
The given information does not indicate that any student was absent from school. Therefore, statement B is false.
Statement C: The distribution is skewed since most students were in the school building for 7 or 8 hours.
As mentioned earlier, the data has a skewed distribution with a longer tail on the right side. Most students spent 7 or 8 hours in the school building, which is reflected by the significant number of X's at those points on the dot plot. Therefore, statement C is true.
Based on the analysis above, the true statements are:
A. The median better represents these data than the mean.
C. The distribution is skewed since most students were in the school building for 7 or 8 hours.