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: 11.6 Median: 12 Mode: 14 Range: 16
BMinimum: 3 First Quartile: 9.5 Median: 12 Third Quartile: 14 Maximum: 19
C
Practice makes perfect
We are given result of a survey in which the customers rated the new menu of a restaurant using a scale of 1 to 20.
We are asked to find the mean, median, mode, and range of the data set. First, let's write the results down in a table from least to greatest.
Survey Ratings
3
7
7
8
8
9
10
10
10
11
11
11
12
12
13
13
13
14
14
14
14
15
15
16
19
Now to find the mean, we first have to sum up all the ratings.
3+7+7+8+8+9+10+10+
10+11+11+11+12+12+13+
13+13+14+14+14+14+15+
15+16+19= 289
The mean is equal to the sum of the ratings 289 divided by the total number of the ratings which is 25.
Now let's find the median which lies in the middle of the data set.
As we can see, the result which lies in the middle of the data set is 12. Thus, the median is equal to 12. Now, let's find the mode which is the most common value in the data set.
Notice that four customers rated the new menu 14. From the given graph we can see that this is the rating which occurred most often. Therefore, mode is equal to 14. Finally, we will state the range of the data set.
We can see that the lowest rating is equal to 3 and the highest rating is 19. Thus, we can say that the rating ranged from 3 to 19. The range is equal to the difference of these values.
Range= 19- 3=16
We found everything we needed! Let's summarize our results.
Mean
Median
Mode
Range
11.6
12
14
16
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.
The median is equal to 12. Next, let's find the first quartile which is the median of the lower half.
We found that the first quartile, or the median of the lower half, is in between 9 and 10. Therefore, the first quartile is equal to 9+102= 9.5. Now let's find third quartile which is the median of the upper half!
The third quartile, or the median of the upper half, is in between 14 and 14. Therefore, the third quartile is equal to 14+142= 14. Finally, let's find the minimum and maximum values of the data set.
Notice that the lowest rating of the menu is equal to 3 and the highest rating is equal to 19. Therefore, the minimum value of the data set is 3 and the maximum value is 19. We found all the numbers needed to make the five-number summary!
Minimum
First Quartile
Median
Third Quartile
Maximum
3
9.5
12
14
19
We are asked to draw a box plot to represent the set of data with the survey results. First, let's the five-number summary that we found in Part B.
Minimum
First Quartile
Median
Third Quartile
Maximum
3
9.5
12
14
19
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.
