BTo find the five-number summary, first write the data from least to greatest.
CTo draw a box plot, first mark all the values from the five-number summary above the number line.
AMean: 149.1 Median: 154.5 Mode: 162 Range: 36
BMinimum: 128 First Quartile: 134 Median: 154.5 Third Quartile: 162 Maximum: 164
C
Practice makes perfect
We are given the data set of Horace's bowling scores.
Bowling Scores
164
128
151
138
158
162
130
162
We are asked to find the mean, median, mode, and range of the data set. To find the mean, we first need to sum all the scores.
& 164+128+151+138+ + & 158+162+130+162=1193
Now, elt's divide the sum by number of scores which is 8.
We found that the mean of the scores is about 149.1. Now let's find the median. To do that, we need to write the scores from least to greatest.
Now that the data is in increasing order, we can identify the median which is the middle value of the data set. Let's split the set into two equal parts.
The median is splits the data set in half, so it is between the values 151 and 158. Therefore, median is equal to the average of the values 151 and 158. Let's calculate it!
Median=151+158/2= 154.5
Now we will find the mode which is the most common value in the data set.
Bowling Scores
164
128
151
138
158
162
130
162
Notice that only the score 162 occurs twice, all the other scores occur once. Therefore, the mode, which is the most common value in the data set, is equal to 162. Finally, we will state the range of the data set.
Notice that the highest Horace's highest score is 164 and his lowest score is 128. Let's subtract these values to find the range!
Range= 164- 128=36
We found everything we needed! Let's summarize our results.
Mean
Median
Mode
Range
149.1
154.5
162
36
We are asked to find the five-number summary of the given data set. The five-number consists of minimum value, first quartile, median, third quartile, and the maximum value. In Part A, we already found the median.
First quartile is in between 130 and 138. Therefore, the first quartile is equal to the average of 130 and 138.
First quartile=130+138/2= 134
Next we will find the third quartile Q3 which is the median of the upper half.
Third quartile is in between 162 and 162. Therefore, the first quartile is equal to the average of 162 and 162.
Third quartile=162+162/2= 162
Finally, we will find the minimum and maximum values.
Notice that the highest Horace's highest score is 164 and his lowest score is 128. Therefore, the minimum value of the data set is 128 and the maximum value is 164. We found all the numbers needed to make the five-number summary!
Minimum
First Quartile
Median
Third Quartile
Maximum
128
134
154.5
162
164
We are asked to draw a box plot to represent the set of data with the bowling scores. First, let's the five-number summary that we found in Part B.
Minimum
First Quartile
Median
Third Quartile
Maximum
128
134
154.5
162
164
Now, let's mark all the values from the five-number summary above the number line.
Now let's draw a straight line between the minimum values and the first quartile and another line between the third quartile and maximum value.
Next, we will draw a box around the median. The sides of the box should go through the points representing the first and third quartile.
Finally, we will finish our box plot by drawing a line inside the box going through the point representing the median.
