Question

Make a histogram of the following data {21, 22, 23, 24, 24, 24, 25, 25, 25, 26, 27, 32, 34}

The shape of the distribution is ___________________________________________________

Use your calculator to compute the mean of the data: __________________________________

Use your calculator to compute the standard deviation of the data ________________________

Give the five-number summary for this data:

Item
Value

Draw the complete box-plot (including fences and outliers). Provide an accurate scale.  

                                                                                                                                                                                                            

Answer 1

Since we know that


Since we know that
Median for a list of even number of data point is the mean of 2 middle most values if we sort the list in increasing order while for a list of odd number it is the middle most value if the list is sorted in increasing order.
Since our list have odd number of data points, this implies that
Median = 25.0
Since, The median is less than mean , so we can say that the the shape of the distribution is left skewed

Since we know that


FIVE POINT SUMMARY
The maximum and the minimum values are as follows
Minimum value = 21.0
Maximum value = 34.0

Since we know that
Median for a list of even number of data point is the mean of 2 middle most values if we sort the list in increasing order while for a list of odd number it is the middle most value if the list is sorted in increasing order.
Since our list have odd number of data points, this implies that
Median = 25.0

Since we know that
The lower quartile(Q1) is the median of the lower half of the data set while upper quartile(Q3) is the median of the upper half of the data set.
Lower half of our list is [21.0, 22.0, 23.0, 24.0, 24.0, 24.0]
Since our lower half list have even number of data points, this implies that
Q1 = 23.5
Upper half of our list is [25.0, 25.0, 26.0, 27.0, 32.0, 34.0]
Since our upper half list have even number of data points, this implies that
Q3 = 26.5
Five point summary = 21.0, 23.5, 25.0, 26.5, 34.0
Min = 21.0
Q1 = 23.5
Med = 25.0
Q3 = 26.5
Max = 34.0

For a box plot, the ends of the box are located at the first third quartiles. The median is the vertical line with the box, The whiskers of the box plot connents the ends of the box to the smallest and largest data values within 1.5 interquartile ranges from the ends of the box. Points outside these plots are outliers.