1) Use these 15 numbers as your data points
141, 330, 292, 198, 263, 224, 149, 121, 223, 125, 126, 48, 111, 327, 238
2) Find the:
Mean=
Median=
Mode=
Range=
MAD (mean absolute deviation)=
IQR(Interquartile range of box n whisker plot)=
3) Create a box n whiskers plot of the data
1) Mean = 192.2, Median = 223, Mode = None, Range = 282, MAD = 76.54, IQR = 105.5
2) To find the mean, add all the numbers together and divide by the total number of numbers: (141 + 330 + 292 + 198 + 263 + 224 + 149 + 121 + 223 + 125 + 126 + 48 + 111 + 327 + 238) / 15 = 192.2
To find the median, arrange the numbers in order from smallest to largest and find the middle number. If there are two middle numbers, take the average of the two. In this case, the numbers ordered from smallest to largest are: 48, 111, 121, 125, 126, 141, 149, 198, 223, 223, 238, 263, 292, 327, 330. The middle number is 223, so that's the median.
To find the mode, identify the number that appears most frequently in the data set. In this case, there is no number that appears more than once, so there is no mode.
To find the range, subtract the smallest number from the largest number. In this case, the smallest number is 48 and the largest number is 330, so the range is 330 - 48 = 282.
To find the MAD, first find the mean of the data set (192.2 in this case). Then, subtract the mean from each number in the data set, take the absolute value of each difference, and find the mean of those absolute values. In formula form:
MAD = (|141 - 192.2| + |330 - 192.2| + |292 - 192.2| + ... + |238 - 192.2|) / 15 = 76.54
To find the IQR, first find the median of the data set (223 in this case). Then, divide the data set into two halves: one half that includes all the numbers that are less than or equal to the median, and another half that includes all the numbers that are greater than or equal to the median. Find the median of each of these two halves. The difference between these two medians is the IQR. In formula form:
Lower half: 48, 111, 121, 125, 126, 141, 149, 198, 223
Upper half: 223, 238, 263, 292, 327, 330
Median of lower half: (125 + 126) / 2 = 125.5
Median of upper half: (263 + 292) / 2 = 277.5
IQR = 277.5 - 125.5 = 152
3) To create a box and whisker plot, we first need to find the five-number summary: the minimum, Q1 (the first quartile), the median, Q3 (the third quartile), and the maximum. We can use the same approach we used to find the IQR to find Q1 and Q3.
Minimum: 48
Q1: 125.5
Median: 223
Q3: 277.5
Maximum: 330
Then, we draw a number line that includes all the numbers in the data set, and mark the five numbers we just found:
<--|---------|---------|--------|--------|--------|-->
48 125.5 223 277.5 330
We draw a box that goes from Q1 to Q3 (the interquartile range), and draw a line inside the box at the median. We extend "whiskers" from the ends of the box to the minimum and maximum. Any outliers (numbers that are more than 1.5 times the IQR away from the nearest quartile) are shown as individual points.
Here's what the box and whisker plot looks like:
```
350 | _
| | |
| _ | | _
| | | | |/ \
| | | | |||||
150 |__|_|____|_||||____________
48 125.5 223 330
```
i don't want how to find the. Mean=
Median=
Mode=
Range=
Alright, here is the box n whisker plot of the data:
```
350 | _
| _| |_
| | |
| _ | |
| | | | |
150 |__|_|___|_____|
48 125 223
```
To create a box and whisker plot, we first need to find the five-number summary: the minimum, Q1 (the first quartile), the median, Q3 (the third quartile), and the maximum. We can use these summaries to draw the plot.
Minimum: 48
Q1: 125
Median: 223
Q3: 238
Maximum: 330
Then, we draw a number line that includes all the numbers in the data set, and mark the five numbers we just found:
<--|---------|---------|--------|--------|--------|-->
48 125 223 238 330
We draw a box that goes from Q1 to Q3 (the interquartile range), and draw a line inside the box at the median. We extend "whiskers" from the ends of the box to the minimum and maximum. The plot indicates the distribution of the data points and shows any potential outliers.
To answer these questions, you will need to perform some calculations and create a box and whisker plot. Here's how to get the answers step by step:
1) Mean:
To find the mean, you need to sum up all the numbers and then divide by the total count of numbers. In this case, we have 15 numbers, so add them all up and then divide by 15.
Mean = (141 + 330 + 292 + 198 + 263 + 224 + 149 + 121 + 223 + 125 + 126 + 48 + 111 + 327 + 238) / 15
2) Median:
The median is the middle value when the numbers are arranged in ascending or descending order. First, sort the numbers in ascending order, then find the middle value. If there is an odd number of data points, the median is the middle number. If there is an even number of data points, the median is the average of the two middle numbers.
Arrange the numbers in ascending order:
48, 111, 121, 125, 126, 141, 149, 198, 223, 224, 238, 263, 292, 327, 330
Since we have an odd number of data points (15), the median is the middle number, which is the 8th number in the sorted list.
Median = 198
3) Mode:
The mode is the value(s) that appear most frequently in the data set. In this case, there is no number that appears more than once, so there is no mode.
Mode = N/A
4) Range:
The range is the difference between the largest and smallest values in the data set. To find the range, subtract the smallest value from the largest value.
Range = Largest value - Smallest value
Range = 330 - 48
Range = 282
5) MAD (Mean Absolute Deviation):
The MAD is a measure of the average distance between each data point and the mean of the data set. To find the MAD, you need to calculate the absolute difference between each data point and the mean, then take the average of those differences.
MAD = (|141 - mean| + |330 - mean| + ... + |238 - mean|) / 15
6) IQR (Interquartile Range):
The interquartile range (IQR) is a measure of statistical dispersion, and it represents the difference between the first quartile (Q1) and the third quartile (Q3) of the data set. To find the IQR, you need to arrange the data in ascending order, then determine the values of Q1 and Q3.
IQR = Q3 - Q1
To create a box and whisker plot, you will need to calculate the Q1, Q3, and any outliers. Once you have these values, you can plot them graphically.
To calculate Q1:
1. Sort the data in ascending order.
2. Find the median of the lower half of the data. If there is an odd number of data points, include the median in the lower half as well.
3. This median of the lower half is Q1.
To calculate Q3:
1. Sort the data in ascending order.
2. Find the median of the upper half of the data. If there is an odd number of data points, include the median in the upper half as well.
3. This median of the upper half is Q3.
Once you have Q1, Q3, and any outliers, you can plot the box plot graphically with the following steps:
1. Draw a number line and position it horizontally.
2. Mark the minimum value, Q1, median (Q2), Q3, and the maximum value on the number line.
3. Draw a box from Q1 to Q3.
4. Draw a vertical line (whisker) from the upper edge of the box to represent the maximum value.
5. Draw a vertical line (whisker) from the lower edge of the box to represent the minimum value.
6. If there are any outliers, mark them as individual points outside the whiskers.
With this information, you should be able to find the mean, median, mode, range, MAD, and IQR of the data set, as well as create a box and whisker plot.