Question

1. For the following set of numbers, find the mean, median, mode and range. Also, find the five-number summary, being the lowest data value, first quartile, median, third quartile, and the highest data value of the given data set. Make a box plot of the data as well. Finally state any outliers. Show all of your work mathematically. Data, the number of conferences each professional of 7 professionals went to in the year 2023: {4, 5, 6, 10, 13, 3, 1}

Answer 1

The mean of the data set is 6, the median is 5, and there is no mode. The range is 12, and the five-number summary consists of the minimum (1), first quartile (3.5), median (5), third quartile (8), and maximum (13) with no outliers. A box plot would represent these statistics visually.

Step-by-step explanation:

To find the mean, add all the numbers together and divide by the count of numbers:

(1+3+4+5+6+10+13) ÷ 7 = 42 ÷ 7 = 6

The median is the middle number when they are ordered from least to greatest: 1, 3, 4, 5, 6, 10, 13. So, the median is 5.

The mode is the number that appears most frequently. There is no mode in this set since all numbers appear only once.

The range is the difference between the highest and lowest numbers: 13 - 1 = 12.

To find the five-number summary, including the first quartile (Q1), median, and third quartile (Q3), first arrange the data in ascending order.

1. Minimum: 1
2. Q1: (4+3) ÷ 2 = 3.5
3. Median: 5
4. Q3: (10+6) ÷ 2 = 8
5. Maximum: 13

Constructing a box plot, we represent the five-number summary and identify any outliers by looking for values 1.5 times the interquartile range (IQR) above Q3 or below Q1. The IQR is Q3 - Q1, which in this case is 8 - 3.5 = 4.5. No number in the data set is more than 1.5 times the IQR from the Q1 or Q3, so there are no outliers.